A massive number of sites have Facebook tracking built in, since FB pays them a fraction of a penny for each visit it monitors. They don't care what username you're using; they just need to correlative fingerprinting (IP addresses, browser/device profile, any data from other apps installed on the same device, etc).

If you opened that arcade, they'd probably recognize that through a couple hundred different datapoints and use that to further analyze user behavior (For example: Which FB/Instagram users went to your arcade, stayed for a significant amount of time, then left. Of those, which don't already own a Quest -- market to them).