I would feel like shit, but it's not "cheating" per say.
Is it unfair? Well, that's debatable. But it's IN THE RULES: you do it, you get a red card and other team gets a penalty. It's not cheating. He did not went around the rules. The rules punish this action.
What in Earth's good name are you even arguing about, do not take this the wrong way, but what do you think cheating means? For me it's the following...
"Cheating is an act of lying, deception, fraud, trickery, imposture, or imposition. Cheating characteristically is employed to create an unfair advantage, usually in one's own interest, and often at the expense of others, Cheating implies the breaking of rules."
He broke the rules because the rules state NO USE of your hands. The rules do not state outfielded players are allowed to use your hands but must be red carded, no where is this ever stated. That punishment exists so no one breaks the rules, he broke the rule, breaking the rules make you a cheat. How can you argue any other way?
Just because you were caught in the act does not mean you were not cheating, it just means you were caught.
Also, I cannot see how your 'thief' analogy works out here.. He didn't steal anything, and that doesn't compare really to cheating :/
You just destroyed the hopes of a billion or so people who were all almost behind just one country. Some can say it was even worse.
And the thief analogy works fine because you say as long as someone gets punished, he is not x, he is still x, he just happened to be caught doing it.
Now you are saying he did an illegal move, an illegal move is considered cheating. If I fitted my car out with nitro in a race that was strictly nitro free, and won it, you would say it was an illegal move, which IS cheating.