Would it be beneficial to create a bigger target for the ldr? You could frost acrylic to so when the beam hits the larger target, the light diffuses and makes the a glowing star (you would have to have the ldr be set to a very sensitive setting). This may work best with your design if you don't cut a hole in the center of the star.
Excellent work done on designing of the circuitry and the star assembly. You have covered everything that should be considered in the design of the constellations. The only worry I have is that in your sample videos, you have already shown how it can be difficult to aim the laser to activate the LDR with a hand-held laser. I am slightly worried on how accurate the players would be able to aim that laser to activate that small LDR while on the sliding platform. This would honestly require some testing.
Another way possibly is to use sensors at the bottom of the platform to be able to sense the orientation of the platform. When the orientation of the platform is pointing in the direction of the stars, it would count as a success.
I had no knowledge of photoresistors before visiting your site, and you made the design really easy to follow. Great consideration for the extra design constraints 5wits provided during the sketch model feedback session.
Its a great idea to move the design to a protoboard. Just be wary of the loose wires connecting to the arduino from the protoboard. It won't be a good idea to use dupont wires if you are thinking of using them. You can get better wires from polulu.com.
What prevents someone from just using their phone flashlight? Does the light from the laser pointer provide more light than a phone? Is there a way to make this game "uncheatable"? Maybe a secondary sensor just outside the star that detects would trip only if an external light was used?
Really liked that you tested out and trialed another sketch model for understanding how the players will interact with it, and where the limits would be for the photocell to pick up the laser.
I love how detailed your concept refinement page is with fritzing schematic, breadboard design and the video showing how it works. Having the list of parts needed in the page also helped to understand the design better.