Interesting question. On the surface, you'd think "no", as Moore is a co-inventor of the MMP. But just under the surface, I believe Moore has assigned all his rights to the MMP to TPL, so I would assume "yes". Would Alliacense press him for a license? IMO, it would depend on how lucrative it might be - to be worthy of kicking sand in his face (i.e., it would be pretty darned rude).
JMHO,
SGE