They're unlikely to work for spinning - most spin bikes use dual sided pedals, cage on one side and spd-type on the other. The spd side will require a two bolt cleat and the shoes don't appear to have 2 bolt fittings. They have the 3 bolt fitting as found on SPD-SL/Look/Time etc road pedals. Note that SPD and SPD-SL are not the same thing. SPD-SL specifically relates to road pedals manufactured by Shimano where as SPD, although originally related to Shimano pedals (Shimano Pedalling Dynamics) has become a term for almost any clipless pedal, but more likely a clipless pedal using a two bolt cleat.
Were the pedals on the bike when you bought it and did you buy it new? If so, they may well be a triangular shaped platform pedal and not intended for clipping in. Do they have a name on them or anything that looks like a spring mechanism?