As per my information "pleasure yachts" are not included into the IMO-Nummer-System, which came into force in 1987
As I understand it, it is indeed strictly-speaking true that non-commercial vessels do not have "IMO" numbers, basically because the IMO regulations do not apply to them. However, like fishing vessels, all sorts of non-propelled vessels, vessels of any type under 100gt, and inland vessels, which also fall outside the IMO's scope, a yacht can apply to IHS-Fairplay (previously LR-Fairplay) for a number. In practice, all vessels which meet IHS-Fairplay's criteria for inclusion in their database (and the printed Lloyd's Register) have a number in the IMO series, more correctly the LR/IMO series.
However, the Equasis database does not cover such vessels.
As Bj