The blue 'G' is Lieutenant Commander Spock (science officer and second-in-command).
The red 'o' is Lieutenant Nyota Uhura (communications officer).
The yellow 'o' is Captain James T. Kirk (commanding officer of the USS Enterprise).
The blue 'g' is Doctor Leonard "Bones" McCoy (chief medical officer).
The yellow 'l' is Lieutenant Hikaru Sulu (helmsman).
The red 'e' is "the guy in red".
Who is "the guy in red"? If you watched the series, it was usually a guy in red that joined the others when they went on away missions (beamed to the surface of a planet). It's usually the guy in red that dies, gets hurt, or messy during those away missions.
Anyways, what's interactive in this logo?
What you see at first is "Google" letters being replaced with different characters as I listed above.
Click on Uhura and you will see a zoomed in version of her... with sparkles to emphasize her beauty (as they did on the show from time to time).
Click on the control panel up front and you will see a light flash. It's usually one of the following (in order): red, yellow, blue, then green.
Click on the door (to the turbo lift) and the red alert light will flash. This takes you to the next scene.
The next scene is the guy in red and Kirk waiting to be beamed (teleported) down to the planet.
Click on the cover panel on the top left to open it and a bunch of tribbles will fall out into a huge pile. (Tribbles are an alien species that look like over-sized colored cotton balls and multiply like crazy. These appeared in the episode titled "The Trouble with Tribbles" season 2 episode 15.)
Click on the the guy in red and he will whine/cry.
Click on the teleport panel and both the guy in red and Kirk will beam down. This takes you to the next scene.
The next scene is the guy in red standing in the background, Kirk standing on the left, and a green 'l' (an alien captain known as a Gorn) standing on the right. This scene is based on an episode titled "Arena" season 1 episode 18. That scene originally had only Captain Kirk and the Gorn Captain, no one else. The guy in red is to emphasize what happens next.
Click on the rock and Kirk will throw it at Gorn. The rock bounces off of Gorn's head and hits the guy in red.
Click on the tree and Kirk will break off a branch to hit Gorn with it. The branch bounces off of Gorn's head and hits the guy in red.
Click on the little pile of junk on the hill and Kirk will climb up the hill, create a bazooka-like contraption, and shoot it at Gorn. The rock will hit Gorn knocking him out, but the remainking gunk from the contraption lands on the guy in red.
The final scene is the guy in red returning from the away mission all dirty and mad.