What do you mean WOULD? I'm sure it IS random? And they presumably just tweak the chance-numbers for some of the monsters for these rare-egg events.
On a completely unrelated note,
I just realized the game had an actual trailer
Well the word "rigged" suggests there is an intentional effort to deceive people about the actual odds of getting a particular item. A perfect example of this is the game BattleLand. They have a similar "pay to roll" system, but instead of this monster pull machine it's a wheel, like wheel of fortune. Every item on the wheel has an equal slice of the pie, but I guarantee you they do not land on the different items with equal probability. Furthermore, a vast majority of the time the wheel is timed perfectly so that it starts to slow down right as it approaches what is clearly the best item on the wheel, only to stop mere millimeters after the end of the best item.
This system is clearly "rigged".
Another type of system which I would call rigged is one in which the odds of you successfully rolling a good item depend on how many times you've rolled previously. So basically the events are not independent of each other.
On the other hand, I feel like with this game the system is more fair. Not in the sense that everything has equal probability, but in the sense a) all the rolls are completely independent of each other, and b) there is no effort to mislead anyone about the odds of getting rare items. I think the odds of rolling any particular item are fixed, and during these special events the odds of a select few items are increased relative to the rest of them, so that they still remain low, but are temporarily higher than they were previously.
Anyway, TL;DR - IMO "rigged" implies either dependent events, or an effort to deceive.