I was wondering if memfd_secret [1] could be a part of a solution to this problem. Sounds like it. Of course, it'd require a recent kernel version, which is an obstacle.
Given that Steam OS is going to be (already is?) built on top of Arch Linux, and supposing that most Steam games that are "Linux compatible" are going to be targeting that as a base platform, this might not be as big of an obstacle as you think (provided Steam plans to keep the OS up to date).
memfd_secret won't help. It only protects memory from being accidentally leaked by the kernel due to an unknown bug. The cheater could easily recompile their kernel to make memfd_secret do nothing.