Ha, I hosted a playgroup yesterday and several of the kids were literally running in circles around our main floor. We have a good loop.

It didn't bother me at all because it helped them get their energy out on a rainy day. My only rule (when at my own house) is no running while pushing wheeled toys around because our son likes to turn that into ramming the toys into our walls/furniture, and if other kids are over there's more risk of getting hurt.
That being said, I understand if your kid is younger/less agile and at risk of getting knocked over by the other kids. The kids at my house yesterday are all the same age and past that stage. You might suggest the nanny try to keep an eye out for it turning into something dangerous for your child if that's a real concern. But if you're just annoyed by the idea of kids running around you should probably just accept that that's what toddlers do. There's a lot of things toddlers do that kind of annoyed me when mine was smaller, but now that he's a toddler I realize you have to pick your battles. So much of toddler parenting is doing what you can to avoid a meltdown.