Yes, absolutely. The Dominion fleet disappearing in the wormhole was de facto
a deus ex machina
This was also my personal shark jumping point
in DS9. ("The plot is resolved with one too many plot twists which are inconsistent with the overall narrative, poorly executed, or are just plain stupid, turning the audience away
The problem with this assertion isn't arguing over a Deus Ex Machina, it's the fact that any other ending to the scenario would have made no sense either with Star Trek's themes or the ones established by Deep Space Nine. For the Dominion War arc to make sense, the Prophets had to play a role (because they're a major part of the show), and it couldn't end in a big space battle.
"Errand of Mercy" is pretty much the Sacrifice of Angels writ large. It's also the basis for Star Trek and war. Star Trek repeatedly highlights that actual military conflict is both useless as well as counterproductive to civilized societies.
Errand of Mercy ends with the Organians enforcing a peace treaty. "Arena" is also about seemingly higher beings enforcing a similar peace. Star Trek is riddled with the idea that "greater entities" view war and conflict as disgusting and we need to move past it.
Virtually all of Star Trek's great moments do NOT end in a space battle. Instead, it's about making peace with your enemy of finding a way around a problem other than shooting it to pieces.
Our heroes winning because of military strategy is about the absolute least Star Trek thing imaginable. If they'd just blown up the fleet with a technobabble bomb that's Anti-Trek in its themes. Asking the Prophets to do it isn't very Trek either, but it's at least NOT a big space battle.
Deep Space Nine's themes (apart from Trek as a whole) are about religion and it's importance. Anti-Roddenberry as they may be, they're a HUGE frigging part of DS9. The Prophets are more important than the Dominion and fans who want to ignore them are sort of missing the point. Like the BSG fans who kept tuning out Baltar talking to God. Yeah, you may not like that part of the show but it's there, it's been there from the beginning, and it can't be ignored.