They can't do that one under their terms of use, at least not directly:
By submitting user content to reddit, you grant us a royalty-free, perpetual, irrevocable, non-exclusive, unrestricted, worldwide license to reproduce, prepare derivative works, distribute copies, perform, or publicly display your user content in any medium and for any purpose, including commercial purposes, and to authorize others to do so
So OP retains copyrights, Reddit has a nonexclusive license to it forever, but only OPs DMCA would be valid.