When I was watching this video I remembered some senior instructors claiming here on aikiweb they teach combat in their aikido dojo. I sincerely hope they prepare their students for the situations like in this video.
Of course this is an edited video showing something very specific...and it's the kind of thing I'd like to see a lot more of because the commercial nature of UFC/etc. naturally shows something more glorious, but I think that's close to being a strawman. Getting in shape "prepares you for combat." The question is how comprehensive they're claiming the activity to be and I think few folks would say they train people how to deal with the best fighters in the world...at least, I've read very few people making such claims.
One thought about the video: I could put something similar together with soccer footage or football...in a similar way do those activities prepare someone for "combat" then?
Another thought: In my own choice of words I would say Aikido doesn't teach people how to fight, but using my buddy's choice in terms, I would have to say it does. I think when some people speak of combat, it similarly means something different: perhaps that explains the gap you see between what Aikido does and what some folks claim about it?