Hm. Yeah, I guess that's a good point. The idea of property can be thought of as "obligations between people", but it's not the same as the idea of the social contract. For starters, it's between individual people, not some collective entity and a given individual, and second, it involves no force as long as no one aggresses against anyone.

Another difference is that the "system of property" actually works to everyone's favour - quite the opposite of "the social contract", and imposes no other obligations on you than to not aggress against anyone else's property. If "aggress" sounds out of place, let's say "interfere with someone's (exclusive) control of their property". There's lots of room for pointless bickering in moral issues, etc.

There are various sensible ways to view the concept of property. One is Murray Rothbard's idea of something becoming your property by "mixing your labour" with it. For example, if you build a house, or plow a corn field, they're your property.