http://bugs.winehq.org/show_bug.cgi?id=26018 and http://bugs.winehq.org/show_bug.cgi?id=17195
As a temporary workaround I prepended "taskset -c 0" to the beginning of my Rift launcher, which isolates the game to the first cpu core. Obviously this is not ideal, and in the second bug I linked it appears a fix for the overall issue is being worked on. Wine 1.4 was just released so hopefully it will be fixed soon.
Additionally, d3dx9_43 from winetricks (d3dx9 didn't install this for me) is now required. After installing I did not need to change any native/builtin settings.