The old or classic definitions would be an 'electric motor', not 'electric engine'...
My first career was in Industrial Controls where 'electric motors' were the
main thing we designed into the project. Some times we also designed in
'engines' and they were fueled by gasoline or diesel
But, it is similar to the general public's misconception to remake or
redefine the original...
Like Silverado used to be a level of trim for GM Pickups (before the
coinage of SUV) and is now a model designation with other marketing
verbiage for trim level...like a Silverado 2500 model with trim level
LS vs the old C20 model with trim level Silverado...
Or that most ICE's has a 'starter motor' that is an electric motor, not
an 'starter engine'...
Difference Between Engine and Motor