Isn't the emperor the chaos god of order? So no even loving the emperor is doing stuff
Not a *Chaos* god, at least not yet (maybe when he dies, but no one actually knows what happens if/when The Emperor dies; different factions have different opinions). It's possible to be a god without being on team supervillain, and the Emperor is as good a candidate as any to being that God.
Besides, to think otherwise is heresy. Only the Inquisition is allowed to engage in such thoughts.
If several win cons trigger I'm not sure what happens, but I imagine it will be horrifying absolutely hilarous.
Let me think....
Imperium finds
Omnicopaeia as Chaos pours out from the Eye of Terror, Orks reorganize under a single great WAAAGH, and Tyrannids finally arrive in the Galaxy in full force. The Ork WAAAGH and Tyrannid super fleet could probably fight each other to a standstill, at least for a while, so they effectively cancel each other out since any fight between them would give Chaos or the Imperium enough time to win. As such, it would be race between Chaos and the Imperium to see whether or not the Imperium can spread knowledge of and utilize the STC enough to withstand Chaos before Chaos overruns Terra and plunges Humanity into an endless night. If Chaos overruns Imperium, they get powerful enough presumably to use Warp shenanigans and Chaos contrivances to win everything. If Imperium builds enough STC shit (which may not even need to be a lot depending on how much OP-plz-nerf stuff they get), Chaos is dramatically weakened (for proof on how this is done, there is a STC fragment that would cure all diseases out there; that's one entire Chaos God made irrelevant), then Imperium uses their super shit to hold the line just long enough to retool for a second Great Crusade (which may include fixing and/or upgrading the Golden Throne, for even more curbstomp goodness).
I think the definition of most of the win conditions is that they prevent the other win conditions from happening. Chaos wins only when everything is daemon world and thus is freaky Chaos shit and indestructible; before then and even if super powerful they can still be routed from existence, after that they are forever invincible until Malal becomes canon again. Imperium *after* bringing an STC back into production would be unstoppable due to the combination of super technology that makes current Imperium super technology look like literal child's play and being wise to Chaos nonsense this time around; but BEFORE the really OP Imperium tech is operational the Imperium could still easily lose to other factions win conditions (Necrons return, super WAAAGH, Tyrannid fleet, etc), it's just that they would probably put up much more of a fight (if the situation is that the Emperor comes back instead of the STC, I don't know what would happen frankly). Orkz seem like their magic powers could win them any fight once they conquer everything, even if super implausible (like killing Chaos, necrons, etc), but before then their mega-WAAAGH would still be defeatable, if only by something like the Tyranids or something. If the Tyranids come in before someone gets off their win, then they eat everything, but if they come afterwards they probably get annihilated by superior firepower or straight up magicked away byy Chaos or Orkz. Necron's old tech is enough to win them any fight, but if another faction wins first they will probably just get exterminated, etc. Everyone except Eldar have a situation where they just rule the Galaxy forever and ever.
In short, the only thing that would really matter is who starts and who finishes out their win first. It would be a hell of a snowball effect, such that any faction approaching the win condition would progressively roll back the other ones and/or slow down other win conditions.