DRK is DynamoRIO as a loadable Linux kernel module. When DRK is loaded, all kernel-mode execution (system calls, interrupt & exception handlers, kernel threads, etc.) happens under the purview of DynamoRIO whereas user-mode execution is untouched — the inverse of normal DynamoRIO, which instruments a user-mode process and doesn't touch kernel-mode execution.
See my ASPLOS '12 paper for the why and how of DRK.