Earlier quoted context omitted.
Not to "both sides" it, but... well, both sides do this in their reporting. Sometimes they also "own" or "destroy" someone. I don't think it's partisan. That kind of language gets clicks, so everyone's optimized for it.
I'm not so sure about it not being partisan. When I think of "own" in this context, it's mostly in relation to "owning the libs." I'm not sure if this particular usage is used mostly by left-leaning pols ironically, or right-leaning pols unironically, however.
[EDIT] downvoters: is this wrong? My perception was that "own" was originally (in a political context—its roots are in gaming, of course) used as a fairly ordinary headline/title intensifier to get more clicks, mostly on the right (for that particular word—everyone plays with language to get more clicks, of course), that parodic use on the left followed, and I'm guessing that its continued use on the right is with some awareness of the way it's been mocked on the left, so has likely changed the intent with which it's employed.