Looks like it can be played on a mac, but do you know the download instructions? If not I'll give you the link to the instructions from OWs Twitter.
I can't troubleshoot from my phone, but when I get home I could see what can be done. Maybe your mac doesn't meet the required system specs?
It says overwatch cannot be played on a mac. Why didn't it tell me that when i went to install it?!?!?!!