It means that I have made a commitment to more than one person.

What is this commitment? There isn't one, any more than there is a commitment you make to a friend.

You mentioned that you consider sexual exclusiveness to be the main defining part of a relationship. I say, the defining part of a relationship is love. Not just friendship but love.

Many relationships exist without love. All of them start without it. That you want love to be the qualifying factor is cute, but it's factually, demonstrably wrong. You can't argue on the basis of what you would like to be true as though it is true.

If they say they're not comfortable then I don't sleep with anyone else.

What if one of them said he didn't want you to sleep with anyone but him? You'd say no? Self delusional nonsense.

Going along that logic, a relationship is basically a contract-I agree to not sleep with anyone if you don't either.

This is correct.

I'm not single because I don't run around sleeping with anyone just because; my partners' well being is more important than simple gratification, and I have agreed to go at their comfort level. I'm not single because my partners have a claim on my time over anyone else.

This is not correct.

I'm not single because my partners and I are planning on building a life together outside of having sex. I'm not single because I am committed to THEIR happiness above my own.

This is obviously self delusion of the highest order. You know in your heart that your partners would be happier if you were exclusive to them, even if they aren't exclusive to you. It's simply human nature to feel envy.

If that's what you like doing, enjoy doing it. I don't judge you for doing whatever you do, it's your life and you should do what makes you happy. But don't kid yourself that what you're in is a relationship.