I don't think you're thinking about what it was like for them to be chastized in public like they were. If you feel that it's embarrassing or negative for them to speak that way to other people why do you have the right to be so negative to them? Why not take them aside when you're not irritated by it, not responding emotionally to it, not confronting them in such a public place? You could have handled this better, and I think your mom is right. You owe them an apology for the way you spoke to them.
They shouldn't be so negative and may not have realized the impact of their words, or how they speak to people. They may need something like that pointed out to them, but certainly in a more construtive manner. I doubt they actually feel like their perfect. Maybe they like to come off that way to others, but most people are at least humble enough to recongnize they are not perfect.
It sounds to me like there are a lot more issues between you and your in-laws than just their attitude at the games. Work it out with them before it festers more...or just let it go. Confronting them in the way you did, allowing it to build up to the point where you lost control of your tone, and embarrassing them in front of so many others was not appropriate.
It also sounds to me like your moms problem with it was that you embarrassed her.