The MOXF is not, strictly speaking, GM compatible. It does have a bank of 128 program listed in GM order and a GM drum kit. But it is not a logo'd GM device. This pseudo-GM bank allows it to respond to properly prepared GM files.

Go to SONG/PATTERN mode
Select a blank Song or Pattern
Press [MIXING]
Press [JOB]
Press [F1] INIT
Mark the box for "GM"
Press [ENTER] to execute
This will setup a GM Template... Hopefully the game data sends the program changes.

This looks like exactly what I was looking for thank you !!

When I press enter to initialize current mix on the song/pattern with GM switch marked, It plays the right instruments sent by the midi file !
There is a limitation though, since a song/pattern seems to have a maximum of 16 MIDI voices, when the MIDI file have like 22, I'm not really sure what happens, it looks like it's taking a piano as fallback for missing instruments or something like that. I'm really novice in that kind of stuff as you may have guessed !
Do you think there is a way to bypass the 16 limit ? I saw an option labeled "chain", can it be... ?

I was using virtual MIDI synthesizers with soundfonts before, thought using a physical synth could be cool since I own one, and honestly it is ^^ I can hear the lag when the instruments switches though ^^

When I press enter to initialize current mix on the song/pattern with GM switch marked, It plays the right instruments sent by the midi file !
There is a limitation though, since a song/pattern seems to have a maximum of 16 MIDI voices, when the MIDI file have like 22, I'm not really sure what happens, it looks like it's taking a piano as fallback for missing instruments or something like that. I'm really novice in that kind of stuff as you may have guessed !
Do you think there is a way to bypass the 16 limit ? I saw an option labeled "chain", can it be... ?

No, General MIDI has a built-in limit of 16 channels. So there is no "like 22" or any fallback for missing instruments, but as mentioned GM is not officially implemented on Yamaha pro synths

Thanks for the information, it has been very helpful on my understanding of MIDI music.
So for a game, if it uses GM standard, it can never have more than 16 audio channels for music right ?
So if there is the need for a 17th instrument for example, it has to replace the instrument of an already used channel ?

There are 16 channels in MIDI. This means in a simple setup you can have a sixteen piece band... As is the case with music some instruments are tacit during portions of the song, you can use a device called a Program Change event to switch the instrument occupying that slot. Perhaps a sound effect is only used during the introduction, after its finished, you can insert a Program Change event to change the instrument on that track.