Uh huh - but when you read those verses in CONTEXT with Heb. 2:16-17 and 1 Tim. 2:5, you see that He is HUMAN (Anthropos) as well as God.
Context is NOT your friend.
You're a cherry-picker . . .
I would put it this way, Emmanuel ! that sums it up, God with us ! that's it in a nut shell and that's why he came and why such can only come as such, or how would we come to know and understand.
Jesus is what he does for us and Emmanuel is who he is.
God with us is about Humans due to the Stain of Original Sin, nothing to do with dogs ect, they do not need Salvation Emmanuel never came for dogs cats ect at all. nothing worse than seeing a Cross above where a Cats buried. or some clown saying that Frits the dog is in Heaven.
No one comes to the Father but through his only begotten Son, So the concept of God is in valid to all who do not come through Christ Jesus, as any other way does not know God.
It's all to do with the Holy Spirit, one that has the Holy Spirit can come to know what Emmanuel is and the Father. all 3 are united as one in the same but have different identity's.
I hear people calling Jesus all the names rattling them off but I stop them and point out, only one that one has to understand is above all that describes him and then what he does comes next. if they do not understand what Emmanuel means, you see they just rattle on and on with names and I say hang on ! Emmanuel is above all them names by far.
Jesus Step father knew that his Name was going to be Emmanuel, Bible points this out.