We probably could run Linux distros under hypervisor (just like default Windows install those days runs not on bare metal, but under Hyper-V).
And then games that wish for anticheat start a separate VM in hypervisor with complete secure boot chain of trust. Would require GPUs to support SR-IOV though.
Maybe something using AI could be implemented - does a screenshot of your game e.g. every second and if it detects anything that would suggest cheating then it informs some central system and sends it a movie of you playing for the final verdict.
Of course this all is based on the assumption that the local AI can do this fast enough with enough precision.