How can I see (and delete) app data for apps that aren't installed?
Yes, you're just syncing the App's data with iCloud, as no files are leftover when an App is deleted. 

iOS apps (and now  OS X  apps too), are Sandboxed. This means that each App has its own space in disk, with its own directories, which act as the home for the App and its data.Deleting an app from the iPhone deletes this sandbox, deleting all data associated with the App.

So, if an App supports iCloud sync, whenever you install that App with your Apple ID, in any of your devices, all the information will be synced.