I decided to make a map of all arcades in Tallinn. First non Soviet arcade appeared after the fall of the Soviet Union (my guess they were brought from Helsinki). My map includes only arcdes that I remember (and know of). Most of them are not there anymore, so no, you can't play Carrier Air Wing in Kaubamaja.
View in Google Maps KML Link
It seems that the most common arcade machine was Neo Geo, but I could be wrong. If anyone remembers any arcades that I didn't mention, please comment ( I'am sure I saw Captain Commando somewhere).