Is God righteous because the rules are His rules?

No to both possible reasons you proffer. Righteousness is the very being of God. God IS righteous. He is uncreated and eternal and eternally righteous. If God did anything unrighteous he would cease to be God. But because he is God, he is utterly righteous. We can't grasp that because none of us are righteous. We are all unrighteous and that's stated in the Bible and why, of ourselves, cannot see the righteousness of God displayed on the cross of Christ. But once the Holy Spirit gives us that understanding, THEN the awesomely righteous being of God hits us like a ton of bricks and we get down on our knees.

According to Deuteronomy 32:4 it shows that all of God’s ways are justice, A god of faithfulness who is never unjust, righteous & upright is he. 

Awesome question!  This is actually a variant of a very old philosophical idea known as the Euthyphro dilemma.  The original wording is akin to, "Is something pious or moral because the gods command it, or is it commanded by the gods because it is moral?"

The first track is basically arguing for divine command theory, which is problematic for a number of reasons.  It makes morality arbitrary.  If god orders something like the murder of children, then it must be moral because He said so.  Although, if you're going to say that God (specifically the one outlined in the bible) is synonymous with morality, I think that is your only option, because we have things like Numbers 31:17 So now, kill all the boys, as well as every woman who has had relations with a man, 18 but spare for yourselves every girl who has never had relations with a man. 

...or a global flood where children as collateral damage was acceptable, or the firstborn of Egypt where it was the specific intent.

For the second track, then God is saying something is good whether or not He says it which has an implication that there exist things at a more fundamental level than God by which even God is bound. In other words, there is a morality that exists and is discoverable independent of God.  There are other similar questions around this like, "Is God bound by the laws of logic, or can he do which is logically impossible?"

You get to an uncomfortable conclusion either way.  I've seen some attempts by apologists like CS Lewis to reconcile this by saying God's nature and morality are one and the same.  But, ultimately, that really isn't solving the dilemma, just putting you on track one.

I've also seen apologists inject, "God doesn't change," to try and diffuse an arbitrary nature behind divine command theory.  But, that doesn't tell us if morality is discoverable independent of God or if it is morality because God said so.  It basically tries to straddle both tracks, but that means you're still got with the moral problems of taking virgins as spoils of war and the like that were already a problem.

Ultimately my solution is none of the above.  Men wrote the things attributed to God.  Some of it was moral.  Some of it wasn't.  When talking about morality, we're talking about actions that maximize happiness and well-being for the majority of a population.  The goal of well-being is a subjective goal, but actions that contribute to or detract from that goal can be objectively measured, because our actions have consequences that play out and can be evaluated in regard to well-being.

Yes, god gets away with bloody murder, because he's righteous.

Dems da rules!

God moves in ways that have been described as 'mysterious'. No one is really sure what this means. Some people think it's because he's a senior member of the Ministry of Silly Walks while others say it's because he's unknowable. The bible itself describes him in all sorts of ways, including "a consuming fire, a jealous God, mighty and awesome, who shows no partiality and accepts no bribes." Quite the guy.

Anyway, the long and the short of it all is that as an entirely imaginary being, not unlike the Jabberwocky or perhaps even a Yeti, there are no rules that confine or constrain him other than those assigned by his adherents. He does whatever his believers want him to.

I do hope this helps.

There are plenty of examples of gods breaking their own rules and acting in immoral ways!

I say "gods", because this apply to MOST gods, not just the Christian god myths!

It is more about His being Supreme and Sovereign. "For He spoke and it came to be; He commanded and it stood firm." "He rules forever by His power." "From everlasting to everlasting thou art God." Psalms 33:9, 66:7, 90:9.

God is righteous because HE created the rules.

He doesn’t have any rules. God is righteous because he is love.

Believers believe God is righteous because they have defined him as righteous.

He has no rules to follow.