If the latest game update is not visible in the Play Store, please try the following.

Clear the cache and data of the Play Store.
This gives the app a fresh start and can help fix issues.
1. Open your device’s settings app .
2. Tap Apps and notifications -> See all apps.
3. Scroll down and tap Google Play Store .
4. Tap Storage -> Clear cache.
5. Next, tap Clear data.
6. Re-open the Play Store and try your download again.

Restart your device.
If you still can’t download after you clear the cache and data of the Play Store, restart your device.
1. Press and hold the Power button until the menu pops up.
2. Tap Power off or Restart if that is an option.
3. If needed, press and hold the Power button until your device turns on again.

If the update is still not available, then read the full article here - https://support.google.com/googleplay/answer/7513003?hl=en