VERY interesting system! But I think it's probably a bit overpriced. You can get the LED strips from Amazon (search for LED strip lights white). Look for 12 volt DC, and avoid any that claim to be waterproof or dimmable. They're under $15 for a 5m (~16 1/2 foot) roll - enough for two strips on an 8 foot garage door.
You can also get 12 volt DC power supplies from Amazon, for example:
The description given at garagedoorlighting.com says the lights come on when the door is fully opened. To duplicate this action, you'll need to mount two spring contacts to the garage ceiling or on one of the door tracks, arranged so they make contact with two metal contact plates on the door when it's fully opened. The use of "open" contacts is safe and legal with the low voltage involved (unlike line voltage).
Alternatively, I suppose you could devise a loop of wire that runs between the garage ceiling and the door opener arm, to maintain contact between the power supply and the LED strips. You could then use a manual switch between the wall and the 12 VDC power supply.
I really like this concept, and may decide to add it to the 16 foot door on the front of my own shop. Blocking light from the shop ceiling has been an occasional irritant when working at night with the door open.