The Chatham manager (and chairman, and possibly owner) is Kevin Hake, who took the reins as a stopgap when Scott Lindsey left and is still in charge, now trying for a third promotion in successive years.
They could simply be supporting a local club (with four ex Gills players) in a big match. Or talking about the ladies' team. Or as you say researching the standard with one eye on a loan agreement - potentially useful if the Chats reach the NLS. Or asking for feedback on Lindsey. I reckon there's zero chance we're considering poaching their manager.