Plus he was sneaking drinks. Remember before Dolores hit him he poorer whiskey in his coke can. I'm sure he drank more often and was not sober.

I'm actually the same way as Joe, and so was my grandfather and great grandfather. I can drink a ridiculous amount of alcohol and barely get buzzed. I've also never had a hangover, regardless of how much I drank the night before. I've also known lifelong alcoholics that fall over after a 6 pack, so I'd assume it's a metabolic thing.
So Joe having that high a tolerance isn't that far fetched. Being an alcoholic probably increased his tolerance to an even higher degree.

Don't forget he drank the whiskey with a platter of food that Delores set out in front of him. That would have absorbed some of the alcohol.

A person's reaction to a substance depends on their own unique physiology. For example; a shot of whiskey would make me sick almost instantly. My aunt, on the other hand, can take two klonopin followed by a bottle of vodka and still remain conscious. She stumbles a bit, but I've seen her go after people. Unsuccessfully, but I guess it's the effort that counts.
Plus, there's the release of adrenaline to consider. Dolores confronted him on the money he stole and his abuse towards Selena. He was a mean drunk, as we saw in the beginning of the movie. So, calling him out on his lies- and threatening to have him arrested- probably set him off enough.
Basically, there are several different factors to consider when it comes substance use. Everyone's different.