Since you aren't using the Google Play Store, you must allow installation from third parties.

Title: Exploring Legacy Mobile Games: A Case Study of Temple Run: Oz – Old Version Download Considerations for Android

Abstract:
This paper documents the process and challenges of acquiring an outdated, discontinued Android game (Temple Run: Oz) for preservation or nostalgia purposes. It covers legal, technical, and security aspects.

1. Background

2. Why Users Seek Old Versions

3. How Users Attempt to Download

4. Risks

5. Legal & Ethical Note
Downloading abandoned games without authorization is a legal gray area. While some argue for "abandonware" preservation, the copyright remains with Imangi/Disney. This paper does not endorse piracy.

6. Recommended Alternatives

Conclusion:
While technically possible to find and install old versions of Temple Run: Oz on Android, users should weigh the security risks and legal ambiguity. For most, official alternatives offer a safer experience.

Released in 2013 as a tie-in with Sam Raimi’s Oz the Great and Powerful, the game was a revelation. It wasn't just a reskin of Temple Run 2. It introduced dynamic environments that were revolutionary for the time. You weren't just running from a monkey; you were gliding on a hot air balloon, dodging the cracks of a crumbling bridge, and navigating the whimsical yet deadly Whimsie Woods.

The graphics were vibrant, far surpassing the original. The "Stumble" feature was refined, and the environment changed on the fly—a precursor to the mechanics we see in modern titles like Surfers or Subway Princess.