The keyboard request you've put in sounds like you would like a mechanical tenkeyless keyboard. It sounds like you would dislike chiclet or membrane keyboards which are usually more low profile. Mechanical keyboards prevent ghosting keys, are usually a lot more sturdy, and have a much farther key travel distance than scissor switch membrane keyboards. Your request for looks cool to a 7-year old suggest you would like backlighting, and it is actually hard not to get keyboards lit up like a Christmas tree for mechanical keyboards at the price range.

10 Ft Cable, and braided with aluminum for durability. Chances are with a cord this long in a common area with a TV someone is bound to snag something on it at some point. This should give you some piece of mind.

Keyboard that matches your request and has tactile feedback. Not a lot of reliable review data.

- RGB blacklit with heavily customizable lighting patterns
- Cherry MX Blue Switches
- Metal-ABS Construction
- 87 tenkeyless
- 35.4076 cm length
First off, this keyboard is 87 tenkeyless and slightly over your 30 cm requirement. The reason I'm also recommending this keyboard is b/c it appears in several syndicated articles as a budget mechanical keyboard and has Cherry MX switches which I'm familiar with and are typing this recommendation with. Cherry MX is a household name for most casual and professional gamers.
Given my familiarity with the switches, reliable reviews I would consider this keyboard as well. Finally, you may want to play a racing game in the future and these typically lend themselves best to using the arrow keys, particularly if there is some sort of gear control on the cars.