Think about it however you want. Obviously the end result is supposed to look like the world's rotating around you; I'm talking about how such an effect was actually implemented, from a technical standpoint.
(Also, I've never actually played Brandish, and the LP in question was a screenshot LP, so I didn't see the effect, either.)
Well, you talk about how it looks without playing any of the games, while I say this after having played (and beaten) the SNES version of both Brandish 1 and 2 (Heck, I even streamed a full playthrough of Brandish 2 SFC.), Brandish: The Dark Revenant and even imported an original PC-98 copy of Brandish 3. I enjoyed (and still enjoy) the heck out of them, so pretty sure I know what I'm talking about.
It is obvious that the screen doesn't rotate since Falcom couldn't do that with the technology at the time (1991~1995), but the games actually work as the way I say (just watch a video of Dark Revenant). I say this because there's no way in getting used to the camera of the Brandish series (sans VT/4 -- that has an isometric camera) if you just keep the mind closed and think "the world turns and Ares doesn't", but only if you keep an open mind and think about it as if it was real life.
Oh and btw, just so you (and more people) can see how Brandish looks and works: Here's an animated gif of the original PC-98 version of Brandish 1 that I made:
See? Ares actually turns, and then the screen does a 90º turn to the direction you've selected. It's a lot easier in Dark Revenant, since everything is in 3D, so turning looks good and it doesn't transition instantly, making people think that it's warpring.
Man, what a wonderful series.
(Sorry if I sound rude or anything, I just want more people to be aware about how great Brandish actually is ;-