At parties held at outside venues like Chuck E. Cheese (actually never held one there), e.g. movie theatre, skating rinks, gymnastics etc., we've usually opened presents at the venue after cake or we've done it at home afterward (rarely). Since the whole point of a party at a venue is to avoid having everyone in the house, the latter isn't my preference. We just keep an eye on the clock and squeeze in the gift-opening. Our parties typically numbered less than 10 children (and often just 5 or 6) though, so it doesn't take that long. If you've got 20 or 30 presents to open, then maybe you should think about skipping the gift opening.
It's fairly common here for people to skip the gift opening. The idea is to minimize that aspect of the birthday party and to avoid comparisons between gifts - which I think is laudable. The focus of the party should be on the fun and celebration and being together.