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That distinction matters because this site has another draw-to-solve puzzle, Save The Pets: Draw to Save, and the two work in opposite directions. There you draw a barrier to stop something reaching a target, and physics tests whether your object holds. Here you draw the route itself, and the test is whether the path you chose touches anything it should not. One is defensive construction, the other is navigation.
The practical consequence is that hazards here are constraints on your line rather than forces acting on it. A dog does not knock your drawing over; it simply occupies space your route cannot cross. That makes the game closer to maze-solving than to physics puzzling, and it means the right approach is to plan the whole path before touching the screen rather than drawing and adjusting.
It carries Puzzle, Kids and Casual. Kids is earned — the premise is reuniting children with families, nothing can be lost permanently, and a single drag covers the entire game. The later levels have real routing problems in them, so it works for an adult too, but the tone stays gentle throughout.