Yes, he's Zod's son, the point of difference though is that in the universe of Earth-2 his father wasn't the same Dru-Zod who we are usually accustomed to.
Think of his father in terms of the Superman of Earth-23 of whom Grant Morrison created - unlike our regular Superman this version is both black skinned and hails from Vultho Island on Krypton. He is Kalel and shares much the same backstory as our regular Superman, with some slight but notable differences. With Val-Zod's parents the differences go one step further than this as instead of soldiers they are scientists firmly dedicated to non-violence. So presumably rather than take up military service this version of Zod was predestined for the world of rational science.
There does appear to be the suggestion that Earth-2's Jor-el may not have been a scientist, nor the one who warns the high council of Krypton's imminent fate. On Earth-2 it is strongly suggested that it was actually Zod and his wife who take the role...
So is earth 2 based on earth Prime then in the NU?
is it that the earth of our kal is the "real one", and that all other earths came spun off from that?