Re-downloading / Installing / Authorizing Previously Purchased Legacy iPod Clickwheel Games

I am hoping to re-download / install some previously-purchased iPod Games onto my iPod Video (model A1136, firmware v1.3).

I have a compatible version of iTunes (v12.6.5.3) to manage iPod games.

The games I am hoping to re-download / install include:

• Sonic The Hedgehog by Sega
• Phase by MTV Games / Harmonix
• PAC-MAN by Namco Networks America Inc.

I had purchased these games originally in 2008

Unfortunately I did not keep backups of these games (as I assumed I'd be able to re-download my purchases). However, any attempts to re-download these games have been unsuccessful.

I even tried using links to the original iTunes Store Pages (e.g. Phase). These attempts have resulted in a "resource not found" error.

There is an archive of various iPod games on The Internet Archive as ipg files. However, it seems that many of these archived games are still locked to the Apple ID of the archivist.

I've tried using my Apple ID to authorize the game (as I have purchased it myself). Unfortunately does not seem to work.

Does anyone know of a way to re-download iPod games?

Alternatively, is there a way to re-authorize the archived version of the game to be associated with my purchase / Apple ID?