Well ... actually .... imperial practice was to identify local gods with gods of the Roman pantheon. The Jewish deity, YHWH, he whom you simply call "God," was identified with several of the Olympic pantheon. Most obvious and common was Jupiter. However, there was even a school of thought that identified him with - get this - Dionysus(!).
Regardless of what we think of the logic of this, it's what the Romans did. A good Roman pagan would have seen the Jewish god as just another name for one of the Roman gods.
I have to do more research on Constantine before I can make any grand assertions. But perhaps at this stage of the game Constantine was still an imperial pagan, the Jewish god simply a local variant of an Olympian god to him, and Christ was simply a demi-god/hero/god-man among many. Remember, the nature and doctrines of Christianity weren't even codified yet, and interpretations of who and what Christ was were open to debate. It was Constantine who had to settle these debates under pressure from his bishops, and methinks Constantine simply wanted token imperial unity rather than any great Orthodoxy when he called those councils.