The article didn't really go into detail about the criteria, but there are some easily quantifiable things that are desirable in a game if it is intended to be

The article didn't really go into detail about the criteria, but there are some easily quantifiable things that are desirable in a game if it is intended to be played 'seriously' (like Backgammon or Go, unlike the games "We didn't playtest this at all" or Munchkin which are just trying to be fun instead of legitimately competitive. A minimal first player advantage, turnabout (ability for someone to come from behind), balance between skill and randomness in games with luck. I think you could come up with metrics for interactivity, eg how much of it is 'goldfishing' vs choices that are notably different based on what the other player has done or will do. Dominion is an example where I think you could show that (for many configurations) an AI that ignores opponents actions would still win some significant portion of the time compared to an AI that takes it into account.