So they want the full game or just the demo?
With all the PDAs I've bought that included games (Same with Desktops) the games were almost always just the demos preinstalled. If you're not getting some money, even pennies on the retail price(A common ratio of monetary exchange when dealing with prepackaged software), but giving out the full product then you've nothing to gain and only more to lose.
After all, the people who get the PDAs who may of bought your software prior now don't have to.
So basically if you're giving out the whole game, you should be recieving some monetary return for doing so. Promotion is useless if you're giving away the whole product.
Btw, it's very common in the Shareware world for large distributors and CD manufacturers to offer, say, $10,000 for the rights to include a full licensed copy of your software on their CD distro, etc. Many highly popular shareware products made their distro numbers through deals like this. You end up with 300,000 units "sold", but only make 30 cents a unit. Doesn't result in large total per-unit profits, but when you concider just how many individual units you have to sell to get $10,000 it's a tasty option.