It is an interesting concept. I'm doubtful that the electric motor powering the compressor would use less energy than a conventional multi-stage turbine but that's not the important part of the demonstration. The important part is it is feasible to sustain combustion using a compact motor built into the engine.

To me this implies that you could theoretically add this technology to conventional designs for performance, efficiency, redundancy improvements.

This would be useful in turbofans as a redundant propulsion system. It would be useful in combat situations to provide an intermittent "afterburner" effect by boosting efficiency. It could also shorten takeoff times and improve throttle response.