In any case, the log seems to imply the Docker daemon is being forcibly killed before completing startup.
I'm not aware of Docker daemon creating an executable file like "/check" that it then runs as an important part of its startup. Seems possible that there is some missing context here, or that this is coming from something else specific to your nodes/containers?
Nevertheless, I can imagine a DIND setup is the exact opposite of what "container drift protection" seeks to deal with in a sense. Docker by design is downloading random executables within layered filesystems, writing them and then executing them. If you are mounting a host socket into these pods, even harder for something like CrowdStrike Falcon to make sense of.
-Chad