http://bugs.winehq.org/show_bug.cgi?id=19226
--- Comment #7 from el elton@schiert.net 2010-08-12 08:51:54 --- Still happens with today's git.
Also, a new observation: The game does not really require you to press both Shift_L and Shift_R. Any two shift keys will do. So if you have two keyboards connected you can press and hold Shift_L on both keyboards and it will grab the piece.