A) Yes, if you buy a game you don’t own the game. Only a license to use the software (in this case the game) was bought. This was, in general, even the case back then when games were sold on cartridges or discs. And it is for sure the case now with digital distribution.

B) Also yes, pirating a game is most of the time not theft but it is still against the law to use a unlicensed copy of any software.