Well, Capcom wanted to do a 3D game, but didn’t have the tools or experience neccessary, so they commissioned Arika to do it.
And since about 40% of the EX staff are Capcom employees that worked on SF2, SF3 and SFA (including Akiman, Nin, and all the important ones), then yes, it most definately is a Capcom game. Capcom staff individuals also programmed, designed, drew, voiced, produced and directed it. Capcom also published it worldwide, and stuck their logo all over it, and in the European version, Arika aren’t even mentioned on the box or manual. So I wouldn’t worry about that too much. It’s as much a true SF game as anything else.
Ultima- as for them not being trilogies- well, I’d count SFA2G as an enhanced version of SFA2. And SFA3U as just a version of SFA3 with extra features. The same goes for SFEX+a. Maybe you could count them as different games, but I’d say they were the same game. They are certainly less different than SF2WW and ST.