Indeed. In League Cup and FA Cup games teams have to wear their league numbers (be it Premier League, Football League, Conference or lower), but in European competition the teams are free to wear numbers in any style they choose, subject to UEFA rules regarding size and stuff.
Generally teams use the current typeface of their kit suppliers to use your club as an example, Arsenal wear the standard Nike numbers when competing on the continent. If the Gunners were wearing a different typeface during their Champions League qualifiers it would probably have been due to the games taking place prior to the new Nike lettering style being released (what with it being pre-season and all). I didn't view all the clip as it isn't really dial-up friendly, but I think the lettering used there was the current Nike style I might be wrong though. 😉