From the mentioned "Japanese Secret Projects" by Edwin M. Dyer III :
" ...nor the Japanese version of the He 162 would progress past the initial design stage. Only the Nakajima Ki-201
ever made it to the construction phase which, by the end of the war, amounted to a single incomplete fuselage.
As a note, 'Ki-162' has been used by some as the designation for the Japanese produced He 162. There is no
historical evidence to sup-port this although it is not without precedent, such as the case with the proposed
Mitsubishi Ki-90 that was to be the Japanese version of the Junkers Ju 90."
So, there really seem to have been a project to build a fighter based on the He 162, but the designation "Ki 162"
is just speculation.