The monsters are summoned via the cards, but the summoning is obviously restrained by rules, likely as part of the contract. Logically if the attack can do any physical damage the Pokemon aren't going to like it. The fact Ash only carries six Pokemon (unless they give him access to his entire PC of Pokemon) definitely is a weakness when Yugi has at least 40 cards, more than half of which are monsters.
Magic cards which mess with summoning and graveyard could be interpreted as playing with the rules of the summoning, so they could argue for not using them. Even so, many magic cards clearly have physical effects (dark hole and Raigeki for example), and monsters go to the same place (graveyard) if they get magicked there as if they get physically killed. Overall, I'd expect the magic cards would still work for the most part.