He hasn't shared someone else's post, otherwise it would say the name of the original page at the top of the post. This one says shared "their" video. If it was a share from another page it would say something like shared "lad bible's" video.
My guess is that instead of sharing the video, he downloaded it, and then uploaded it to his page. Perhaps this is an older post and he has decided to share it again on his page, which is why it says "shared their video" at the top.
I could be wrong on this, because I haven't seen it quite like this before. But you can get the same result by just downloading the video and uploading it to your page. That way it just looks like your own post and the "like" button goes to your page.