Is it possible to play Xbox 360 games on the Xbox series x if the series has a Xbox 360...

if the rumour has any truth to it, it will be an Xbox exclusive (Xbox One and Series X and possibly 360) as there has already been a press release stating that there wont be any games exclusive to Series X.

Yes, if you purchase the game from the Xbox 360 marketplace, you can play it on the Xbox 360, Xbox One or Xbox Series X|S.

As for what Hardcore Games said, you can still buy Xbox games for the Xbox 360, and play them on the Xbox 360, and if they are backward compatible, play them on the Xbox One & Xbox Series X|S.

the whole family from 2001

Xbox

Xbox 360

Xbox One

Xbox One S

Xbox One X

Then soon Xbox Series X and possibly Xbox Series S

I totally understand, however, the game has its own version that can be played on Xbox One or Xbox Series X|S and the 360 version game is not backward-compatible, even if we want to it is not designed to be played on the Xbox Series X|S console.

If you are trying to play Xbox Series X|S games from the Game Drive, then that is not possible. The only way to play those games is from the internal storage or the official Xbox Series X|S external storage cards. The Game Drive can be used to play Xbox One, Xbox 360 & Xbox original games via backward compatibility.