This is an old video from 1991 that bears the name of the (very young at the time) Studio Gainax. The feel is a bit like an end of year student project but it is very well made. Although this video is a "trailer", Gainax never produced an R20 anime, although a Manga bearing the name does exist.
WMG Music's copyright bots apparently found this video, so now the soundtrack has been replaced by silence. Sorry.