Yes and no. An electric compressor doesn't mean the turbine doesn't drive the fan. (It might make pre-cooling easier.)
Maybe the transmission losses aren't relevant if you're thrusting for a short interval?
> transition from turbofan to turbojet to reach mach 2.7 to allow starting up a ramjet
Oh. Cool. Sounds like an air turboramjet [1]. Plus a fan?
Not sure how you ditch the fan, nor why they'd describe an electric motor driving the fan as an electric compressor. Granted, I skimmed the video.
The loss in the electrical system should be pretty small, and they claim that they gain a lot of efficiency from being able to optimize the engine over the whole range from 0 to mach 2.7.