D.B.
Is he doing a mitzvah project? A lot of synagogues require kids to do 13 hours of some sort of community service. That can be the theme for the centerpieces. My son collected sporting goods for a couple of local agencies dealing with underprivileged kids - he set up a donation bin at the temple, went to local stores requesting donations (he had a letter from the rabbi saying it was a legitimate project), and he got a lot of new and gently used stuff based on the needs of the agencies. We collected everything and turned them into the centerpieces before giving them away. So people sat at the "hockey table" (with used hockey skates) or the "soccer table" (with new and used soccer balls, cones, etc.) or the "baseball table" with gloves and mitts and wiffle ball bats. We had a "back yard table" with frisbees and badminton rackets. So if your son is doing something that has a built-in theme, he can use that for centerpieces.
For the gifts, we only gave to the kids - we found a candy store that sold chocolates wrapped like soccer, basketball and baseballs, and gave each kid an assortment. It's not our custom in this area to give personalized gifts to every attendee so I'm not sure what your area is used to. Most people understand charity though - and it fits in with the Jewish value of your son joining the community as an adult and taking on adult obligations, including tikkun olam (repair of the world) and tzedakah (righteous giving).
Sometimes people collect toiletries for food pantries and battered women's shelters - use a plastic bin and fill it with purchased items or donated items. Ask area dentists for toothbrushes and sample-size toothpaste tubes. Or use donated canned and boxed goods for the local food pantry and just number the tables rather than dividing things up by category. A lot of synagogues suggest at 3% donation to Mazon, the Jewish response to hunger. So donate 3% of what you are spending on food and goodies for those who have little or nothing. Your son can ask for donations in his invitations (which means he's giving up a lot of his gifts, which is okay), or he can solicit the neighbors, or he can put a notice in the synagogue newsletter or set up a booth at the local supermarket (get permission from the market) saying he's giving to the food pantry in your town.
As for games, what is the structure of the party? DJ? Usually they have games that are routine - "Coke/Pepsi" is almost required it seems. You can also rent things at the rental company or sometimes borrow (for a small fee) from the school department - the thing I see a lot at parties even for graduation are things like beanbag tosses and something with 2 balls on a string that you toss and try to wrap around a crossbar. Not sure what it's called but it's everywhere and something all ages can do. You could check with a rental company to see what their biggest sellers (or rentals, actually) are.