"avatAr is not in the vedas, so it refers to a man that the Almighty God has sent".
With this, he sets the false premise that an avatar is actually a man sent by God, and builds on that. He says that the vedas talk about the Rishis, who are God 'sent' to guide the humankind. He then compares this idea with the prophethood as mentioned in the abhramanic religions, and then connects the two dots - that avataras are actually rishis who are sent by God, in parallel with Quran. Uff. This is called arm twisting of the truth.
In the Gita, Sri Krishna says in several places that He is the Supreme Lord: example "aham sarvasya prabhavaH, mattaH sarvaM pravartate" (I am the Lord of everything and everything comes from me); that He is "mahEshvara"; that He and His true nature "cannot be perceived by the tained/naked eyes because the intelligence is covered by the illusory energy"; that He is the only one to be worshiped; that every action is to be submitted to Him alone. A prophet cannot make such claims, only an avatara can.
From the Islamic perspective, the above are the claims made by 'Allah' in Quran, so Muslims should not have much issues in accepting Sri Krishna as the Supreme Lord - God Himself. I respect them if they cannot acknowledge and accept this as truth, because as Sri Krishna Himself says - that is their intelligence level and He provides that which matches their level.