IIRC, Yamaha style files technically are MIDI files, although they do include proprietary types of "chunks" in addition to their standard MIDI chunks. The MIDI standard says that MIDI-compatible devices should just ignore any data chunks they aren't programmed to recognize and respond to, therefore you could try simply renaming the files to a ."MID" extension, then try using the renamed file with your other keyboard or software to see if it works.
An alternative would be to use the Style Split and Splice software to separate the style file into two parts, the standard MIDI part and the proprietary part.
Style Split and Splice - The Unofficial YAMAHA Keyboard Resource Site
www.jososoft.dk
Either way, the standard MIDI data might be difficult to work with, since the style's musical data will be in the form of one-off style sections (intros, fill-ins, and endings) as well as sections designed to be played as loops (the main sections), so it isn't as though you can simply play the MIDI data from beginning to end like a song.
Plus, most of the musical data will be transposed to the CMajor7 "key" and is designed to be dynamically transposed to other keys and chords as the keyboard is playing the style, in response to the keys and chords that you're playing in the accompaniment section of the keyboard.
Add to that the fact that the voices and kits used by the style will be ones that are available on the Yamaha model that the style came from or was programmed for, so the Bank Select and Program Change values will need to be converted to suitable equivalents for the target keyboard.
The kit voices (drum kits and sound effect kits) will be especially tricky, since kit voices are designed such that the specific sounds to be played are specified by the Note values, so potentially you will also need to transpose some Note events to other Note events in order to select a reasonable substitute sound from whichever kits you have converted the Bank/Program data to select.
