You have deduced correctly, the time that steam tracks is the entire time a game is a child process of steam. Since the tracking of this is consistent cross-platform, it appears to be the intended behavior by valve.
Heh... I don't think I'd assume that consistent is the same as intended or desired, but thanks for letting me know the problem is not linux-specific. I'd submit a bug report on a tracker for cross-platform issues if I had access to one.
Closing as this is expected.
Nothing extracted yet.
I recently noticed that Steam for Linux claims I have been playing certain games for over a hundred hours, which is grossly incorrect. It seems to be counting hours during which the game is sitting at a menu screen, in a background window, on a hidden virtual desktop (aka workspace). Any one of these conditions should pause the play time counter, but apparently none of them do.