|In this game, only the dogs are relevant players.|
So, the small dog was being strategic because he took into account the big dog's preferences:
outside > treat.
He took into account person's preferences:
being hassled by dogs, opening door often > dog piddling on carpet.
To get what he wanted, the small dog figured out what the big dog and person wanted and then manipulated both so that he could get some time to get access to what he wanted.
Hence, the dog was being strategic--knowing his preferences, knowing the other players' preferences and then acting accordingly.
And, yes, I miss the hell out of these two dogs, especially the smaller, smarter, more manipulative one.