Online competition is great, but as any gamer who grew up in the 8- and 16-bit era can tell you there's nothing like fragging your friends when you're all in the same room. It adds a much more personal and enjoyable element to any pixilated contest.
If your little gamer enjoys the thrill of Xbox Live races, kid-friendly fighting games, platforming or even deathmatches, cater to his competitive (or cooperative) nature and love of video games.
It's an underused feature, but two Xbox 360s can be connected to each other via wired system link, and you can actually link between three and 16 consoles together (for up to 64 connected players) if you use a network router or hub.
Regardless of your method of connection, you're going to need a TV and copy of whatever game they're playing for each Xbox. But if you can convince all the party attendees to bring over their consoles (and maybe a small television), you'll be hosting the kind of birthday party that schoolyard legends are made of before you even press start.