I get that perhaps you feel that the child will be upset at not getting gifts, right? But surely the parents have told the child what's going on. It's not your responsibility, frankly, to worry about that end of things. That's up to the parents. I actually would think it impolite to bring a gift if told not to. A handmade and heartfelt card would mean more.
With so many kids showered with tons of stuff, parents are trying to make events about the activity itself, not the swag the kids will receive. Maybe they're trying to teach the child that the party is, itself, their one big gift.
My daugher's having a birthday party soon, a bigger event than usual, and I"m going to ask her to forego gifts in favor of something useful like donations to the local food bank (which is desperate for food right now). She is older so she understands that she can do without stuff. It really is not unheard of for parties, even for kids, to have either "no gifts" or to request that in place of gifts, guests bring donations for food banks or even pet shelters. I've seen both done and applauded it.