How do I download a game on another account without a purchase history of the game in it?

If the game was installed on a different account, you need to install it from the account that purchased it. If you do not have access to that account any more, you will not have access to those purchases. Further more, attempting to access that account
for that game/purchase history could be considered fraudulent activity if you don't have permission to be accessing the account or do not own it at all.

If the account was yours and you can no longer access it you can try to reset the password or recover the email address associated with it. Here:

https://support.xbox.com/en-US/my-account/microsoft-account/forgot-microsoft-account-solution

https://support.xbox.com/en-US/my-account/microsoft-account/lost-password-solution

If you do have access to the account, sign into it, go over to the ready to install section of the menu under the "games and apps" section, and you should be able to look for it and find it. The child account should have access to it then. You could also
try using the "Home Xbox" feature with the adult account.

https://support.xbox.com/en-US/games/game-setup/my-home-xbox

If you may also need to change the privileges on the types of games the child account can play. When the passkey that usually locks children out of changing their own privileges is forgotten, or listed as forgotten, it often resorts back to the account password.

https://support.xbox.com/en-US/my-account/security/create-xbox-one-passkey

unless you have your xbox set as home, there's no way to access a game with an account that didn't buy it.

If you're using an Xbox One, have the adult account set the console as their Home. That will allow you to share gold/games with the child account. https://support.xbox.com/games/game-setup/my-home-xbox

Otherwise, the game would have to be purchased on the child account.

If you purchased the game with the gamertag that you are posting with then it should be in your Download History.

Go to Settings>Accounts>Download History and you will be able to redownload the game without incurring another purchase cost.

Are you definitely using the same account that purchased it on 360?

Check your download history here:

live.xbox.com/.../history

If you do not see Minecraft there, it was another account that paid for and downloaded the game originally; you will need to use that account on the Xbox One to get the reduced price.

Let us know how you get on.