The "big ones" like Unity, Cryengine, Unreal etc. include many many things. They are absolutely huge compared to what a single game using them actually needs. A game engine is just that: an engine for games to run on to seperate engine and gameplay programming.

If your team decides to create singleplayer game(s), and your own engine as a platform for it, then building full networking and netcode into that would be out of scope. That would still be a game engine nonetheless.

Can the term game engine include networking? Absolutely. Does game engine inherently imply networking? No, I don't think so.