Load-bearing walls often support the weight of a floor above or trusses for the roof. When you remove a load-bearing wall, you need to provide an alternate method of supporting the weight--or risk severe damage to the house (and perhaps life and limb, too).
Is the wall's non-continuous nature a clue? No. A wall can be non-continuous and can still be load-bearing.
For this, we need to know the direction of the joists for the floor above.
