Piggybacking this chost, since I don't directly have a second anime opening game. Closest I can think right now is Love & Destroy, where the cutscenes are basically an anime episode. BUT:
Anime openings were all the rage for a while. They used to do them all the time, especially once the Playstation 1 era kicked off CD storage that you could blow a few dozen MBs on. Tech Romancer, on Sega Dreamcast here, was a Mecha fighter that had a super secret second anime intro that they didn't want you to know about. (you could unlock it) The art was produced by Studio Nue, who are most known for the Macross franchise. Back when Capcom still made games, rather than just re-release them. They used to do that, too
Read More has the full intros, just for you👇