Oh I love that. I've been watching it for years on youtube. Great mixture of athletic ability and musical interpretation and the formations are always so tight. Incredible.
Yes, that's the Japanese version, which assumes that flexibility is for the girls the same way that tumbling is for the guys (in a good way). But there's actually a different type, that appeared in Spain.
From what i've read, some love it, some hate it. I still have mixed feelings, and I think the mixed version looks more like dance or acro, so I'm not sure if it should become a sport...
Read an article yesterday about their being women competing in every event that the men do at the Olympics, but not the other way. There is no male rhythmic gymnastics or synchronized swimming. Apparently some men have petitioned the IOC to make some changes, but I don't see it happening. I googled male sync swimming, and all I could find was some drunk guys joking around for their wives. I don't know how seriously the petitioners are though.
ETA: Just watched the videos above. Some of that looks more like dance than gymnastics to me. I'm not convinced.
Most of those aren't rhythmic gymnastics. Rhythmic gymn involved apparatus, like the ribbon. Without it, it's a separate thing entirely. Most look more like group gymnastics or team acro or dance rather than rhythmic.