I found that if you make the game on the Scratch website, there is an option on itch.io to add an external file where you can put the games URL in. This basically turns the Download button into a play game button
Heres what I did specifically on my game
1. Set 'Kind of Project' to Downloadable
2. Select 'Add External File' (it's to the right of the 'Upload File' and 'Choose From Dropbox' buttons)
3. Change type from Executable to Source Code ( I don't think this step really matters, but just in case)
4. Copy and paste the URL for the game into the 'http://' section
Hope this helps!