Applications of these two ideas could include enabling the player to see his or her progress in earlier games within the latest sequel, being able to keep the same character/progress across games, etc. etc.
While the best solution is likely having the player create an account they use across games, I'd like to avoid that if I can (both because players are already logging into Google Play Games, and because I currently do not have access to server infrastructure to handle doing that). Is there any other official/popular mechanism for passing data between games, or is the account route the best bet?
I believe that this is what you are looking for, Interacting with Other Apps especially the Sharing Simple Data and Sharing File section. You may also refer to this documentation for Receiving Simple Data from Other Apps which suggests that you will need an ACTION_SEND intent filter.
Update Your Manifest
Intent filters inform the system what intents an application component is willing to accept. Similar to how you constructed an intent with action
ACTION_SENDin the Sending Simple Data to Other Apps lesson, you create intent filters in order to be able to receive intents with this action. You define an intent filter in your manifest, using the<intent-filter>element.Handle the Incoming Content
To handle the content delivered by an Intent, start by calling getIntent() to get Intent object. Once you have the object, you can examine its contents to determine what to do next. Keep in mind that if this activity can be started from other parts of the system, such as the launcher, then you will need to take this into consideration when examining the intent.
I think this would be a good place to start on how to pass data from one app to another. You will also need to make changes in your current implementation both in your existingt and new app for this to be possible.