The actual vertical weight of the bike is carried by the wheel ledges that aren't immediately obvious in the main pic. Even medium-duty drywall anchors are rated for a vertical weight of up to 75-100 lb, so a 30 lb bike split between two drywall-mounted wheel rests would be well within the specs for even light-duty drywall anchors (although as an inveterate overbuilder, I'd rather anchor them in studs if it was an option) The horizontal force on the pedal mount (the "weight" of the bike leaning out away from the wall and attempting to pull the pedal mount fasteners out of the wall) would be a function of the bike weight and the lean angle, I think it might be the sine of the angle so, assuming a 30 lb bike at a 25 degree lean, and the pedal level with the center of gravity of the bike, we looking at 30 lb x 0.42 = 12.6 lb - the horizontal component would be less if the pedal is higher than the CoG, and more of the pedal is lower, but I don't know how to calculate that. Since you're looking at horizontal force on the pedal mount fasteners and vertical force on the wheel ledge fasteners, if it came down to it, I'd put the pedal mount fasteners into wood, and would be fine with the wheel ledge fasteners in drywall.
In any case, the forces involved are pretty minor