I think Periscope aligns more with Twitter's "live" vision. But yes, it's definitely next if anything.
It definitely does seem to align better. It was pretty interesting watching the debate on their platform and I can imagine sportsball getting more involved there as well
I watched a sportsball on Twitter once and it was really the same as ESPN's site or the pirate streams from reddit, once you fullscreen it. Just another live stream, there (thankfully) wasn't any Twitter integration popping over the sports.