The recorder is an “inner channel flute”, so it is a flute with a whistle mouthpiece. The flute family is large!
We understand that this can cause confusion, but the name “Recorder Master” didn’t really seem appropriate to us (and was already taken at the time). For most English-speaking people whose native language is not English, “Recorder” is simply a device that records sound, as this is the most common definition.
In addition, 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, it is a game about (soprano) recorders. A real “flute”, i.e. a transverse flute, will not work with Flute Master.