For every new offer, DomainAgents.com sets a 7-day limit to respond. The buyer waited until the last day to respond. It is a game because the buyer is acting as "Well, I like the domain name, but I'm playing it cool and acting like I don't care."
I, too, play the same game sometimes: "Well, I don't have to sell the domain name, but if you offer me enough money... I will consider it". Just because I play the same game does not mean I like playing it.
I actually like dealing with corporate lawyers more. They are very straightforward, and usually, after a few back-and-forths, they will tell you either the client doesn't have the budget or they are moving on in a different direction.
Even more context: the domain name is a 5 letter word .com, it was used as a startup name (the founder wanted to buy it at the time but could not get approval from the VC, and it later went out of business), The name was used as a marketing agency, and it is a somewhat well-known Italian name.