Apple, who believes the iPhone could also be a popular gaming platform, has definitely been center stage for digital distribution of software in general. It wouldn't be accurate to say that they entirely inspired the move, however, as numerous companies have been knee-deep in digital distribution in some form or another for quite some time – including both Nintendo and Sony. As far as handhelds go, though, it may be all Apple's fault. Any company that has been on the fence about combining digital distribution with mobile devices has had the Apple iPhone App Store prove that the time for such offerings is now, not years down the road.
One thing that has occurred to me is management of the software people buy. If you own a handheld console, a regular console, a PC and perhaps an iPhone, you have at least as many online stores to keep track of. I wonder if in the future there will be a market just to manage all these intangible online purchases.