It looks like there is an API call to view the users that watch a repo from [GithubDeveloper]:(https://developer.github.com/v3/activity/watching/#list-watchers)
List watchers
GET /repos/:owner/:repo/subscribers
Is there any way to see this list on the site? Am I interpreting the API correctly? Is watching equal to subscribing?
When on a repo's page, you'll see links on the right side in the "About" column that give you this information:
Or go to this URL directly:
https://github.com/{user}/{project}/watchers