Additional linkages or linear path is not needed.
My goal was to merge A-arm and fork suspension into one hybrid system, make it (maybe?)better and stroger and still make it look like a bike (hence the fork shape).
A-arm is there to take most of the impact forces and make the virtual steering "tube" legth or fork turn axis much longer compared to traditional fysical tube in motoframes. That longer distance between support points makes bending moment forces much smaller. With that you don't need beefy steering tube and bearing and upper frame = lighter structure and lower CoG.
Fork (as said before is not necessary to be shaped as a fork) is attached to the frame and A-arm with ball joints so the fork can move with the A-arm in arc path. A-arm is -10 deg in neutral position so ski pivot point direction during suspension travel is up and backwards in gently sloping arc. That fork tube/slider acts just like linear moving upper A-arm with infinite radius but you can steer the ski through the system without any additional joints between handlebar and ski and that is a good thing.
During suspension travel the steering angle becomes less steep which calms down steering feedback during big bumbs and hard landings. Front shock has rising rate instead of linear rate in normal forks.