Can I play Forza Horizon on Xbox 360 that I purchased digitally on Xbox One

Hi, unfortunately Forza Horizon 3 is available only for the xbox one, therefore is impossible to play with it on the xbox 360... if you are unable to use it also on your pc, you can try to contact the xbox support in order to verify if you can get a refund,
you can contact them here: https://beta.support.xbox.com/help/...games-apps/digital-game-purchase-refund-terms
(on the right you have the button "contact us")

If you want to buy a similar game for your son you can try to find a copy of forza horizon 2 (available also for xbox 360), you can try to find a phisical one (be carefoul that you need a copy for the xbox 360) from amazon or other shop or a digital copy
on the xbox marketplace here: https://marketplace.xbox.com/en-US/Product/Forza-Horizon-2/66acd000-77fe-1000-9115-d8024d530aa4

Moreover note that a digital copy of forza horizon 3 can be used both on xbox one and windows 10 since it is a xbox play anywhere game (more info here: https://www.xbox.com/en-US/games/xbox-play-anywhere),
unfortunately forza horizon 2 is not available for PC.

This covers what you need to know:

"Forza Horizon was delisted from the Xbox Live Marketplace on October 24, 2016, and can no longer be purchased. Owners of a physical disc can play the base game on either an Xbox 360 or Xbox One, but they will not have access to any digital content.

Those that own a digital copy of the game, and any related downloadable content, prior to its delisting can reacquire any purchased digital content through their account purchase history or their Xbox One dashboard."

https://forza.fandom.com/wiki/Forza_Horizon#Downloadable_Content

If Xbox Series S digital can play Forza Horizon 4 online it means that there shouldn't be any problem with other games that aren't free and that's okay if we will not set it as Home Xbox. It's just odd that you're getting that error with Forza Horizon 5.

If I may ask, were you able to obtain the game through a game pass or did they purchase it digitally?

Do you have Forza Horizon on a physical disc, or as a digital download?

Only digital downloads provide ownership for both systems.

Also as Ackis already mentioned, make sure you bought Forza Horizon 4 on the same account that you use on Xbox One and PC.

If you bought it on a different account that has your console set as "Home Console", all accounts on the Xbox One can play the game on that console, but not on the PC.

Only the account that actually purchased the game digitally can download it on Xbox AND the PC.

Yes, purchased the XBOX ONE version and I'm signed into the same account on the Xbox as the PC. I can see the other games we've downloaded digitally on the PC but only Forza Horizon 4 appears on the Xbox.