Given that valve refuses to use KLA for their own competitive multiplayer games, and has gone out of their way to not make their hardware locked down, I really dont think they will go down the path of making a locked down platform or facilitating intrusive anti cheat.
A TPM is entirely under your control. It's designed in such a way that you can't do certain things with data within it, but that's not because (at least in theory) someone else can and is controlling your TPM to prevent you from doing those things. The TPM, unlike an installation of Windows, doesn't only listen to Microsoft.
Similarly, the presence of unsigned software on a computer would not stop a Linux kernel level anti-cheat from working, and the kernel level anti-cheat shouldn't prevent the unsigned software from working. Once you run that unsigned software, your machine is tainted similarly to the way your kernel is tainted if you load the NVidia driver.
There are several products that rely on a USB device like this for DRM solutions. It’s probably much easier to unlock static assets than validate running code, but I don’t have insight on the true complexity.
What does the USB stick actually do? The hard part of implementing the anti-cheat (ie. either invasive scanning or attestation with hardware root of trust) is entirely unaddressed, so your description is as helpful as "would it be possible to implement a quantum computer as a USB stick?"