But since they knew they needed him, had him born through what could be called (in the broadest sense a rape) they knew they were going to have to save him. Looking at it in that sense that they were going to make sure he fulfills his destiny for them, takes all the tension out of the series. They intervened to protect him from a situation that would kill him. Sounds pretty close to DEM.
Uhh, that last sentence is a complete non sequitur. What you're saying is that it removed the tension because it was a predictable and inevitable extension of what had been established elsewhere in the series. That's the exact opposite
of a deus ex machina, which is a resolution that is not
based on anything previously established, that has no logical connection to any prior story thread.
Also, I disagree with the rest of your analysis. Yes, it's a given that the Prophets needed him alive; they said as much in the episode. But the key point, the thing that makes it a meaningful character conflict, is that they and Sisko disagreed on how
to achieve that goal. The Prophets urged Sisko not to sacrifice himself, to avoid taking on the Dominion fleet singlehandedly. But he stood up to them and refused to submit to their will. He forced them to bend to his
will for a change.
This is the mistake being made by people who think it's a DEM. They're focusing on who performs the key action, which in this case was the Prophets, but that's not what matters from a story standpoint. What matters is whose decision
, whose will and desire, is responsible for bringing about the outcome. Stories are driven by wants and needs. The Prophets' wish was for Sisko to avoid confronting the Dominion fleet, and for themselves to avoid intervening in mortal affairs. That's what would've happened if their will had predominated, if they'd been the decision-makers here. But they weren't. It was Sisko's will, Sisko's decision, that prevailed. He chose to confront the fleet and forced the Prophets to intervene more aggressively in order to save him. The outcome was a direct consequence of the protagonist's own initiative and choices, and that is anything but a deus ex machina.