I can't see why not. M7613 should be the 3rd revision with a DVI connector (rev 1 and 2 were DB-15 and VGA connectors respectively), so it should work fine on a new Mini using just a DVI <-> Mini DVI adapter.
There's confusion between the three revisions and the model numbers though so even if it's either of the other two connector types, it should still work with adapter/s - VGA will require a VGA <-> miniDVI adapter, and DB-15 will require two adapters: a DB-15 <-> VGA adapter attached to VGA <-> miniDVI adapter (and I have no idea if anyone's ever even tried that!).
Apple's ever-changing display connector types keeps the adapter industry in business. 😉