As others have said, call and find out what the hostess is thinking. Here's a story for you....
My son was in a rather new school, where we didn't know the kids and their families real well, yet. All the parents were super nice, it's just that we had only known them for about 3 months, since moving to the area. My son was in ice skating lessons, and decided to have his birthday party at the rink where the lessons took place. We set it up and invited about 10 boys. We had a friend in town who would be bringing her son and said she would stay at the rink with us. It didn't even dawn on me that at this age (5), parents would do the drop off. Each parent came, said hell/goodbye/see-ya-soon and left. I kept thinking at least ONE of them would stay. Nope. We had a party room and I was there, greeting guests as my husband was down on the ice. I kept thinking my friend was going to show up any time to help watch the kids and be an extra set of eyes/hands. She ended up being very late and her hubby decided not to stay home with her baby, so was there with a 10 month old . I was getting nervous as to how we were supposed to keep track of all these kids! The rink was open to the public and there were quite a few people there, besides us. I had a 2 year old and 4 year old, too! My husband and I were worked up into a literal sweat, running around, doing head counts, etc. Some of these boys couldn't skate at all, and I was so nervous someone was going to get hurt!! I was right. One boy caught a skate blade to the cheek, which resulted in just a "flesh wound", superficial scratch, but I was a wreck. His mom was entirely cool about it, but I felt awful. Now, we recall that party and laugh, but at the time, I was completely taken by surprise by the fact that none of the parents stayed. Since then, even when though my kids are older, if it's a public place, I have parents mostly staying. We didn't do public area parties for quite awhile after that..LOL! Just recently, my daughter had a party at a roller rink and I made sure I had back-up! Most of the parents stayed, even though I didn't "ask" them to.
If you know of another parent who might be staying, you could ask him/her to help keep an extra eye on your son, if you feel comfortable. Most of the ChuckECheese-type places have safety systems in place to keep just anyone from leaving with a kid, but at a more adult establishment, there may not be one in place.