If Google Play shows Open instead of Update for Cradle of Empires, the cause is usually the Google Play cache or a Google Play Store app update. Clearing the Google Play Store cache and data should help to resolve it.
Let's try the following steps and see if it helps:
1 - Go to device Settings > Apps > Google Play Store > Storage
2 - Tap Clear cache and then tap Clear data
3 - See if you can update the game
If that doesn't help, please try the following:
1 - Go to Settings > Apps > Google Play Store
2 - Tap Uninstall updates
3 - See if you can update the game
If you still can not update the game, please send us an email to support@awem.com and describe issues you got, the more detail, the better.