Yeah, Reddit hasn't really changed the API itself with these recent changes, they just made the keys to it cost money.

An API is basically a communication standard between the app and Reddit, that standard changes as new features are added or decisions are made. The app might make a request like getvideo and expect to get a video with the .redditvid extension. Now let's say Reddit decided to fix their shitty video player and now they start rolling out a new video format, .redditvidgood, and update the API so that getvideo returns this new type.

Now the app makes a getvideo request and gets a .redditvidgood video, but it has no idea how to handle this format, it's still expecting the old .redditvid format. At best the app will fail to load these new videos but still function otherwise, at worst the app will crash any time it tries to load a video. In this example, even with the best case scenario most videos don't work anymore. It's only a matter of time before a change completely breaks all apps that don't update for the current API, and only a dev with the source code can make those updates to the app.