I have that exact stick. It is Ps3/PC compatible, and will play on PS4 games with the legacy drivers (SFV works fine). The stick is NOT ps2 compatible. I don't think they make an adapter that goes from usb, back down to ps2 (i know they have one for the reverse).
That being said, it's very easy to mod with a ps360 akishop, or a toodles/mc cthulu (if you don't need 360 support). The only downside to modding them, is you cant take off the panel from the top...have to undo the base, and then remove the top panel....aside from that...great stick, and also EASILY upgraded to a sanwa JLF stick. (may have one already in it by default, I cant remember honestly)