I thought the definition of racist was believing that one race, ethnicity, or culture group was superior to any other.
No. That is wrong even for actualized racial favoritism, which "racism" usually denotes, as there does not need be a formulated belief or even a direct comparison.
"Your new build didn't turn on? Gosh, you must be an idiot."
"My build didn't turn on? Goddamn Newegg sent me broken parts again!"
"Your kid is an Eagle Scout, was decorated for pulling a family out of a burning building, and was accepted to Harvard at 16? Neat how some kids are born with poise and drive."
"My kid turned out... umm... hey, he's not a serial killer! Oh, yeah! All me. Best. Dad. Ever."
I don't need to know your standard to invent and use a self-serving double standard. There can be an innate affinity for the self-serving, it need not be the effect of an overt belief.
"I am right and you are wrong."
"No, I am right and YOU are wrong."
"Well mine is right because, as it is self-serving of the superior being, it is superior."
That one would probably prompt someone to check themselves. This one even more so: "Mine is self-serving, self-serving is superior, thus I am right, thus I am the superior being."
Racism is pernicious because, as the expansion of self-centeredness into ingroup bias, its entry is usually in the unexamined choice of premise, not in the logical argument to follow.
"A white man saw a black carrying a gun in his neighborhood and shot him? Wow, I hope my neighborhood has such heroes! Said he was in fear of his life? Who wouldn't be? Good shoot. You have to protect what's yours. This is why we need guns to protect ourselves."
"A black man shot a white man as he was out walking? What is this nation coming to where a man can't exercise his Constitutional right to free movement without getting shot by some animal? They say he had a gun? What is that supposed to excuse in an open carry state? The killer didn't know the law, plain and simple, and he shot a completely innocent man. He was probably a racist just seething with envy looking for any reason to take out a white. This is why we need more guns to protect ourselves."
You don't need to have a formulated belief in racial superiority to be a racist. An affinity for conveniently shifting the goalposts in your favor and you have your "I'm not a racist," racist.