http://bugs.winehq.org/show_bug.cgi?id=58280
--- Comment #3 from Rafał Mużyło galtgendo@o2.pl --- I don't know anything about Mass Effect, but on a chance it's Unreal Engine or something alike, see if changing wine's renderer from 'gl' to 'vulkan' helps.
It's rarely the case, but you may get lucky.