This problem is not unique to browser games. To play a game or download it from a devlog, you have to visit the game page. There is actually a link from the devlog to the game page (where it says Food Grade Bananas » Devlog under Music loops!), but it’s easy to miss. This list of files at the bottom of a devlog is strictly informational.
That said, I agree with you completely. It would be a lot more convenient of the list of files at the bottom of the devlog were links.