It's a "jet" in the sense that it doesn't have a visible propeller, which is really the only meaning that word has any more. Virtually all the thrust produced by aircraft that people call "jets" comes from shrouded fans of some sort.
What useful definition of jet am I missing (beyond the trivial "can't be electric") where this can't usefully be called a jet?
Designers (of subsonic devices) rapidly moved to a more efficient turbofan design where the exhaust provides very little thrust and the engine core is used as merely a torque engine to turn a rather larger shrouded fan which actually produces the thrust.
So... if you pull out the internal combustion engine and replace it in a straightforward way with an electric motor that drives the same shaft, are you really changing the nature of the device?
Just like "turbojet" derives from it being a turbine-powered jet, I think the new electric version should be called a "magnejet". Or just "jet" for short.