Not sure where you looked on McMaster Carr but it's there:
https://www.mcmaster.com/#roller-chain/=16g8g8s
Fixing with a new master link will work, at least for now, but remember that chain has been stressed over it's whole length and the "weakest link" failed so now the second weakest link will be next inline.
Do you know how to adjust the tension on the chains?
Edit: Not sure why the link to the chain does not go right to the chain page. But when first page opens click on the "Roller Chain and Links" then at the next page click on the "ANSI Roller Chain and Links" that will give a list of all the chain sizes. Scroll down the page and it will show the "Heavy Duty Chain" which should be what I would go for for a skid-steer. 80H, sold by the foot. Just measure yours and go from there.