It’s legal to have a ROM of a game you actually owned and ripped. This is simply allowing the ROM that you actually own to be played on a different console, the web.

In this case, the user is distributing the ROM which is illegal. But the method to make it work on the web is fair use. The legal way to do it would be a website where users “insert” their own rom and the website simply lets you play that ROM on the web.