Translation:I play football, you play tennis, and he swims.
Not really, no.
But thanks for the question, it made me realize something.
We may choose between "és" and "pedig" depending on what we want to emphasize.
"Én focizom, te teniszezel, ő pedig úszik."
This sentence simply describes what everyone is doing. Emphasis is on the verbs. We will never emphasize "pedig" in this position, so it lends itself naturally to this pattern.
But imagine the other situation, where it is about who should do the various activities. Maybe nobody wants to swim, so we try to make him do it. Or this is a special triathlon, and we want to re-assign the three events as best fit our talents:
"Én focizom, te teniszezel, és ő úszik."
In this case, we want the pronouns, including "ő", right in front of the verbs, in the emphasized positions. Which is best done if we use "és", not "pedig". "Pedig" would separate "ő" from the verb.
You're asking a question as old as the chicken and the egg, mate. I'm an Australian so we're kind of in the same boat regarding what shaped ball constitutes a "football" vs a "soccer ball", but from an outsiders perspective American football seems to make precious use of the foot. On another note, if you watch Touch Football, the kicking of the ball is not allowed at all. Weird.