We don't know if the creators of the Doomsday machine were destroyed by it. In fact we don't know anything about them.
I don't know if the Kelvans were defeated, it's more like they were shown that they had different interests from those who sent them.
The Providers made a wager, mostly to fight boredom, it seems. When you make a wager there is always the possibility to lose. I don't know if there is anything ironic about it.
The minosians and their weapons seems to be the only example of yours that's truly ironic.
You are partially correct about the Doomsday Machine, that we don't know exactly who built it from anything like, say, a license plate with "Iconians" (as an example) on it, but the audience is encouraged by the words put in the mouths of the characters to accept Kirk's explanation and as far as I am concerned this makes it so, as far as storytelling is concerned. Thus, irony.
We can quibble about whether to call what happened to Rojan and the other Kelvans a defeat or not (and I don't think the Kelvans' superior technological prowess and thus likely extreme superiority to the Feds/AQ in warfare was ever in doubt), but the fact remains their plans of conquest were thwarted, and by their
own methods. It seems to me that the episode goes to great lengths to point it out--it is the heart of the episode, really, that having human form, they feel too human and thus empathize too much with the real humans as well as desire too much of what the real humans desire to be true to their orginal Kelvan selves. That is irony.
The Providers' only pleasure was gambling on a raw, physical contest, and they kidnapped and forced other sentients to fight to satisfy it. Then they were beaten at THEIR game and by THEIR rules--and the little pastel mushroom-cauliflower-looking bitches even tried to rig the game BY their rules. And Kirk still handed them a defeat. And, and this is the kicker, they didn't lose one to each other, to another Provider, but to one of their kidnapped thralls.
They created all the circumstances of their defeat at gambling, and were beaten by a lowly thrall, and the contests they created served to eliminate their contests. If this isn't being hoist by your own petard, which is a saying that encapsulates the meaning and essence of irony, I don't know what is. It's irony of the first water.