Explaining the problem with a column of values from a non-mutually exclusive domain
The best argument against the existing design is that there's really no good primary key on the table (except perhaps an identity column, which I don't consider a good primary key). That makes it hard to join to other tables.

An advantage with your design is that a query can easily identify parcels where you (for instance) have mineral rights but not surface rights using a simple WHERE clause. With the existing design, this is still possible, but it's a lot messier (and not really feasible using graphical tools or entry-level SQL). This is particularly important if the table in question is a dimension table in a datawarehouse.