When David died then his son Solomon was king. When he died then his son became king. And so the line of Davidic Kings go down to the current Davidic King. The tribe of Judah is still here, and so is the bloodline of King David.
To suppose that bloodline no longer exists is not reasonable. It is like saying that DNA is not in the Bible so it does not exist.
Davidic Kings have the Davidic Covenant at their disposal. Meaning that they can sacrifice themselves for their people. Which is what Jesus did on the eternal scale. But traditionally they only facilitate the covenant temporally. Most however are not able to use the covenant due to their wickedness.
So yes Jesus was a Davidic King while in mortalaty. Therefore he is one of the Davidic Kings. However, he is God Almighty which is more than a Davidic King. His covenant is eternal.
Since you do not accept the current Davidic King then you will not be protected under that covenant. You do have salvation in your personal covenant with Jesus Christ however.