Sounds like a single layer 3 network but multiple layer 2 data links. Usually 'internet' is reserved for networks connected by a layer 3 device but a layer 2 device still has to make 'routing' decisions between the data link layers, which is usually called 'switching' and not routing.

I'm not sure if there is a common term for an aggregate collection of switched data link segments, perhaps "layer 2 network"?

In any case, using "internet" to refer to connected layer 2 data links isn't a particular strong abuse of the term in my mind.