Classic Tumblr: the only site fucked enough to let you edit other people's posts. Try all you want, Twitter, you can’t possibly add a worse feature than that.
You can't edit the post on someone else's blog, but you can when reblogging it to your own. This means that anyone who rebloggs the post from you, someone who reblogged from them, or anyone else down the chain will retain your edits. It was really popular to do this to John Green.
I think it's just taking a well-known (or maybe copypasta) thing and reposting it with edits. Like if I just
Classic Tumblr: the only site great enough to let you improve other people’s posts. Try all you want, Twitter, you can’t possibly compete with Danny Devito.
EDIT: Though this has the same replies as the Markiplier one, I'd guess someone just mixed the screenshots of the newer post and the reply chain of the other. So 3 levels deep (original, edit and chain, permutation).
No, there was a period of time on Tumblr where you could actually edit other people's posts when you reblogged them. The edit would only appear in your chain of posts (i.e., your reblog and if anybody reblogged your edited version), but it would be completely indistinguishable from the original unless somebody went and viewed the original post on the op's blog or something. No quotes or acreenshots needed. Simply hit reblog, scroll up, and change the original post however you like, then hit post.