We enhance the pointed quandle counting invariant of linkoids through the use of quivers analogously to quandle coloring quivers. This allows us to generalize the in-degree polynomial invariant of links to linkoids. Additionally, we introduce a new linkoid invariant, which we call the in-degree quiver polynomial matrix. Lastly, we study the pointed quandle coloring quivers of linkoids of $(p,2)$-torus type with respect to pointed dihedral quandles.