How is a flight routed from the last waypoint of a STAR to final?
Look more carefully; says it right at the bottom. At the STAR's termination waypoint, LGA, expect radar vectors to final.

If you had comm failure, and couldn't talk to ATC, you would fly the STAR in your clearance and if it is an open STAR like that, at the termination waypoint you would find your own way to the ILS/LOC and shoot the approach, taking the most logical path to get there and avoiding any unusual maneuvers or turns.

A lot of the procedures you see in SIDs and STARs are not followed exactly as depicted when ATC is giving instructions (the controller may put you on vectors long before you reach the termination waypoint for example), but are there in case of a communications failure, to ensure that an arriving or departing aircraft has obstacle clearance and so that ATC can predict with reasonable certainty where you are going to go as you arrive with no way to talk to them.