Zangief - Dhalsim honestly isn't too bad for the big guy from an objective point-of-view in Street Fighter V, but... by the end of the day it's still a nuanced match-up that requires a particular playstyle. What Zangief has to do, much like any other character really, is know how to counter-poke or whiff punish to cope with his limbs if Dhalsim is successful at keeping his opponent at bay. Of course it won't be as cut-and-dry in an actual match, but here are a few examples to illustrate the above:
Now keep in mind that these aren't his only options, so I recommend looking into it yourself when examining your options or ideal spacing in Training Mode. The above came
from the basic guidelines I wrote on how to play Dhalsim, and I peppered it with some advice on where his weaknesses lie by design if you want to educate yourself about what he's capable of. How much you need to know naturally depends on how good the opposing player is, which is why I linked the guidelines, but your core gameplan against your run-of-the-mill Dhalsim will revolve around three pillars as Zangief.
1) Knowing how to respond to his teleports
2) Being aware of when his slides are punishable (as they're very unsafe)
3) Having a method to work him into the corner (which is where the counter-poking will come in handy)
TELEPORTING
First and foremost: contesting the teleports is relatively easy if you're fighting one who is overly aggressive. A common misconception is that this move gives him impunity to approach people, which is far removed from reality. Every character in the game has multiple buttons to stuff him out of it on reaction, with most characters also having methods of escaping a post-knockdown mix-up, but let's go with the safest universal option here for the sake of clarity.
If he's teleporting a lot, condition yourself to jab. If he brings himself next to you (be in front or behind you) then even his fastest attacks will lose to your standing jab, which in turn puts him in a 50/50 situation as soon as he touches the ground. Against most characters with a command grab, this is a
terrifying prospect for Dhalsim; things can easily go wrong just off of one wrong guess with all the considerations he has to make in a split second. His quickest normals (standing LP and LK) are 4 frames instead of the usual 3, so if your frame traps are on-point, he has little choice but to endure the block string against most characters. This naturally carries an inherent risk against someone like Zangief, since if he's looking to defend himself against Zangief's buttons, he has to worry about the inherent threat that is the SPD in conjunction with even a normal throw. You can say he has access to a V-Reversal, but this can be baited out (a net positive for multiple reasons) and subsequently run the risk of being grabbed out of it. He can reversal teleport away from that 50/50... but in Street Fighter V he can now be grabbed out of this too. Dhalsim could backdash out of Zangief's SPD... but then he's automatically susceptible to counter hits or even worse, a Crush Counter.
What if Dhalsim teleports in place instead? Jab anyways, because there is flatout nothing Dhalsim can do to punish a whiffed jab from that distance. Hell, even during fireball set-ups it can occasionally be worthwhile to jab him out of the teleport in spite of taking the hit from the projectile, because you will usually recover in time before Dhalsim can retain control again. Note how the Bison is walking forwards when Dhalsim is still airborne:
Apologies for the .gif being on the quick side, but it does highlight there being an opening. Another factor worth bringing up on how to control his teleport hijinx, is the fact Dhalsim
cannot teleport behind you if you're at the very edge of the screen if your back is as close to the 'corner' as possible, thus making his options all the more predictable. I say 'corner' because this works anywhere on the level. Lastly, refining your reflexes against a teleport isn't exactly a difficult ordeal: your mileage may vary, but the way I do it is via audio cues. His teleport has a very sharp sound to it, higher pitched than most other special moves in the game, so it ought to be second nature to jab (or whatever else works) through this alone without even
seeing his destination once you're accustomed to this.
SLIDES
Combating the slides is comparatively speaking quite straight-forward. Know this:
without near-perfect spacing, these are all punishable on block and sometimes even on (counter) hit! This extends to his Yoga Drills too with less severity, but I digress. Now of course the Dhalsim could aim to only have them hit you at the last active frames of the move, but it's not something a whole lot of them are currently doing right now, so learn how to exploit this weakness until they learn. It is without a shadow of doubt a bad habit prone to heavy punishment, with his HK slide being the only true exception here (for some characters) if it's blocked by the very tip of it given the distance between both players afterwards. If Dhalsim's V-Trigger enters the equation, things get a little more complicated however. Slides can be made safe with its activation, which is why most Dhalsim players rely on it as a crutch, but thankfully Zangief is one of several characters that can nullify the flame carpet through a well-timed V-Reversal. The 'trick' here is to execute it during the flashy V-Trigger animation where the opponent is temporarily frozen, as seen below:
CORNER PRESSURE
Admittedly this is a weakness that every character suffers from, but this is an important aspect to dismantling a Dhalsim for a variety of reasons. The choices that he can make here are severely limited, even moreso if you have the situational awareness to lower the effectiveness the above two pillars I listed.
Staying grounded is crucial: Dhalsim has 3 - 4 strong anti-airs covering different distances, never mind that his fireballs as well as his air-to-air normals (read: V-Skill) provide him a lot of control over the air space. Jumping isn't always a bad idea and you should definitely test the waters whether the Dhalsim has the presence of mind to make any jump-in attempts borderline redundant, but you have to respect this strength vs a skilled one, especially with Zangief having a shallow and slow jumping trajectory on top of his actual size. Two concrete examples as to when it can be a good idea to jump regardless of player ability: if you want to trade with his anti-airs given the health discrepancy between both characters, or if you want to move closer in between the opening of let's say 2 x standing MP from Dhalsim. If he throws non-EX fireballs, you can dash under time with the right timing.
Even the act of simply walking forwards and doing nothing (save for timely blocks) can cause the other player to flinch or hesitate when you're an imposing heavy-hitter.
Now to get the actual point:
counter-hitting and whiff punishing limbs make for an exaggerated twist on footsies, but it is key to pushing Dhalsim towards the corner and which is why I stress you ought to opt for a grounded approach. It forces him to be more considerate about his actions, maybe even second-guess himself long enough for you to inch closer if he lacks the mental fortitude or experience to get around this, effectively turning the match-up into a war of attrition. This is emphasized by the noticeably prolonged animations and recoveries on his pokes compared to their equivalents in older Street Fighter titles. With correct timing you can even get a knockdown with Zangief's sweep if you read a standing MK or Fierce Punch, or better yet even a Crush Counter! If it's the latter, you're only two forward dashes away from being in his face before Dhalsim is allowed to stand up! With his back against the wall, this is where Zangief can truly press an advantage if not victory itself: Dhalsim's close-range normals are adequate, but they're liable to being outpoked by other character's normals when put on the defensive. As a result he has to be careful when he's actually pushing a button, lest he run the risk of Zangief eating some hits with help of his armor moves, being shimmy'd by those with movement speed or falling for frame traps including potential Crush Counters. Knockdowns lead to meaties that he cannot exactly escape from in this position either. V-Reversals, teleports and slides come with their own (aforementioned) caveats with the latter only really being useful to low profile under jumps; another reason to stay grounded! Bottom line of this match-up is:
make your corner pressure count, because while it can take a ton of work to put him in this position to begin with, while he's there Dhalsim struggles to make an escape against mindful players. No easy get-out-of-jail cards, period.
TL;DR
I know this isn't exactly the type of advice you were specifically looking for, nor did I watch your replays, but I wanted to point out that the match-ups you were struggling aren't necessarily lopsided on a fundamental level in Street Fighter V thanks to its immaculate balance. If you lack the know-how to get the ball rolling, then that's understandable because Zangief has always been one of the more demanding characters to perform well with. Regardless though, hopefully the above information will be of use to you concerning core tactics / mindsets and gave you enough insight on drawing parallels with his other problem cases.
Sure. I'll contact you if I spot you on Steam.