It’s a bit more complicated, really. The islands weren’t usually politically united. China lost actual control of the Ryukyu kingdom well before the first Sino-Japanese war, but maintained a claim on it for quite some time.

The US took over administration during WWII and converted many of the Japanese bases to American ones. The US doesn’t claim any of the islands anymore and has closed some installations, but a lot of bases are still active. The US is responsible for Japan’s defense. Japan would rather have the bases in Okinawa rather than in mainland Japan (although there are a few bases there as well), which a lot of Okinawans feel is unfair. Okinawa is very well placed strategically though and Japanese people don’t like foreigners (sort of… It’s weird), so don’t expect the situation to change any time soon.

BTW, if you ever want to visit Japan, Okinawa’s a great option. It’s beautiful there and it’s not hard to get by on just English.