Ex parte literally means "without notice". It's what you use when it's an emergency - there's no time to explain! - or if you served the other party they'd cover something up or do something nasty (say, a domestic violence case, or child abduction).
It is, shall we say, not a good match for a dispute like this. This round is over now (judge is already declaring it moot, although I don't know why, did they just let a temporary order expire? There's not a lot readable on the docket yet).
Importantly, No-IP now may have a clear shot at a pretty vicious countersuit, because what MS requested in their TRO (which has not been continued ahead of the hearing on... Thursday? I can't read US dates well...) caused them, and their customers and the internet at large, damages - serious, huge, actual reputational damages with people moving away from their service which thrives on high uptime and reliability. They had no opportunity to answer the case against them - the action MS requested the court make against them was unilateral, which is... unusual.
MS will probably try to climb down in the most graceful manner they can, and settle out of court. However, No-IP will not want to accept a token settlement for MS destroying their business: on the face of it, they have a very strong case and I doubt MS will be able to offer enough to compensate their ire, so we'll probably see a countersuit instead, and - speculation - it'll probably not go well for MS at all, unless they have hard evidence that No-IP were actively complicit in abusive activity, which seems to have been what they (mis?)represented to the court in their TRO application (but we're missing that particular piece of the jigsaw, because it was sealed; and again, it shouldn't have been sealed). If MS had that, however, I speculate they wouldn't have dropped the TRO ahead of the hearing, and that prospect, shall we say, seems unlikely overall compared to the prospect of them making a huge mistake.
Huge company attacking small business - that's a powerful angle. They might even be competitors of No-IP, thanks to Azure (and the gimped version they used to host these domains clearly couldn't hold a candle to No-IP, because all the domains were down). If I ate popcorn, I'd be getting a bag, but don't expect Thursday to be fireworks. I actually expect it to be de-listed as moot and the action dropped until No-IP countersue, and they could take their time on that - in fact, they might want statistics of how many of their customers jumped ship on having their domains down for several days at MS's whim. And they might want another jurisdiction, 'cause I gather jurisdiction shopping is a thing over there?
MS might've got lucky with the judge. They're not necessarily going to keep being lucky.