I don't think economic means that it has to involve the exchange of purely material goods and services. I use the term because I tend to see a relationship as a bargain between two (or more) people with the end goal of obtaining happiness. Each person brings a wide variety of goods to the table, not just physical goods like cash, and a house, and sex, but emotional goods like support, conversation, companionship, and higher principles. A relationship then turns into an extended bargaining session between the participants in which they compromise and agree on what to do, with each participant remaining in full control of their assets. I don't believe that anyone owes anyone else anything at the start, but rather that people should come to a settlement, sometimes by bargaining (I'll do the dishes if you cook), sometimes by compromise (I want to go to Florida, and you want to go to Alaska, so maybe we'll go to New York), and sometimes just by gifting (I'll help you out just because I want to). I believe that at any time, any one of the participants can say "No, I don't want to bargain this away."

Maybe it says a lot to me that I tend to think of relationships as an evolving system of bartering and bargaining, but I do think that both people have to decide how best to use what they bring to the table. To me that act of constant compromise and continual bargaining seems profoundly economic, just not one that involves cash.

(I learned economics in a very broad school where the definition of the field was essentially the study of how you used your available resources to obtain your desired ends. Under a definition that broad the game theory interaction between two people can almost always be seen as economic - but not monetary).