Not even close to the extent you need to have it for a fast-paced AFPS. Watch some top-level quake gameplay and compare it to top-level Overwatch gameplay, it's night and day. Hell, some OW characters even aim for you or don't need to aim at all to be effective (Winston for example)
>but now there are a host of other mechanical, tactical and cooperative skills to master on top of that
Cooperation sure, OW does put more of an emphasis on teamwork. But as far as mechanical and tactical skill goes I don't see how you can make that argument unless you've never played an AFPS