Most non-Muslims tke the word Muslim as to mean someone following the religion of Islam, which includes the belief that Muhammad was the last & final prophet as per the sha'ada.
People like Moses, Jesus, Adam etc did not follow the Islamic religion as per today,although they do fulfil the emboldened above., but there certainly didn't say the sha'ada.
So my point is that saying to non-Muslims that these people were Muslims is a little disingenuous when conversing with non-Muslims.
ETA So under your definition above, Jews & Bahais, who also claim to be submitting to God, are also Muslims? Right?