A recorder is an “inner channel flute,” so it is actually a flute with a whistle mouthpiece, - the flute family is large, and this can easily cause confusion!
For most English-speaking people whose native language is not English, a “recorder” is most commonly defined as a device that records sound, so the name “Recorder Master” didn’t seem appropriate to us (and was already taken at the time). On the other hand, Portuguese, for example, refer to the recorder as “flauta” (or “flauta de bisel”), which is much more similar to the word “flute”. This is also the case in many other European languages.
But, of course you are right, - the game is about soprano recorders. A real “flute”, or a transverse flute, will not work with Flute Master.