The kernel people at https://bugzilla.kernel.org/show_bug.cgi?id=70411 told me
this needs to be fixed in mesa, so here it is.

The interesting part:

01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI]
Wimbledon XT [Radeon HD 7970M]

Latest mesa git, but has probably been happening since HyperZ was enabled by
default.

dmesg is attached there: https://bugzilla.kernel.org/attachment.cgi?id=125651

It's reproducible every time so I can later get more detail. For now there's
the dmesg: Starting the game and showing some intro works, but shortly before
displaying the menu X freezes for a few seconds and after it is usable again, I
see the stuff starting at 82688.801309 in dmesg.

HyperZ seems to work fine for everything else I have tried so far. It only
happens in the Distance Alpha that's only (officially) available to kickstarter
backers.