Miles and Mrs. Peel, in lieu of seduction, play a board game. It looks like Ludo, a simplified version of Parcheesi, which was in turn derived from the 1400 year old Indian game of Pachisi. It might be Uckers, which is a variant of Ludo highly popular with the Royal Navy (and an odd choice for an RAF man).
To foil eavesdropping microphones, the defense trio zip themselves into a large bag. This episode aired almost one year after the pilot episode of Get Smart introduced 'the cone of silence', which served the same strategic and comedic role.