It's [supposedly] humorous because if you were to give your right arm, you could no longer be ambidextrous.

A somewhat dull oxymoron. Another one of this kind would be "I'd die for the chance of living that moment."

He is/was a baseballer. Ability to throw/catch with both arms is an obvious advantage. THe paradox of losing one arm to be able to keep using both is what makes this funny

He would pay any price (idiom -give his right arm) to fulfil his wish of being ambidextrous - he ends up in oxymoron, which is funny.

Being ambidextrous (as opposed to strongly right or left-handed) would solve a lot of problems (e.g. cutting fingernails). "I'd give my right arm to..." is an idiomatic expression meaning to want something very much.

to give the right arm means "to pay any price for something", ironically in this case, for being ambidextrous (to be able to use both hands equally well)

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I would give my right arm (= I'd do absolutely anything) to be able to use both hands with equal facility.

A set expression: "I'd give my right arm to {whatever}". Once again, Yogi comes up with something funny to plug in. (By the way, the desire to be ambidextrous is common among baseball players.)

In baseball been ambidextrous as I am, is a privilege among the baseball players, so is a good translation for this or any sport, due to the big advantages of using both arms and have the same strength, and abilities to throw or bat.

We shall forever remember him.