Glad your son succesfully assembled it! The Hackvision is essentially an Arduino. I'll add some clarifying comments to the game development page, but as for the explanations about the Arduino IDE, bootloader, and compiling/uploading sketches, that's covered best on the Arduino site. Hackvision has a ATmega328 chip, so choose "Duemilanove or Nano w/ ATmega328" on the board menu. I will definitely clarify that.
Do you have a USB-serial FTDI cable or adapter? That's needed for uploading your own games.
You've got the concepts right -- the bootloader allows the IDE to communicate with the chip and upload firmware programs ("sketches"). It will hold one at a time, and yes you can always compile and upload the original Hackvision firmware. This firmware and required libraries are on the game development page in the section "Downloads". For explanations about how/where to install libraries, see the Arduino libraries page
Writing games does assume some familiarity with Arduino and experience in C programming. I'd suggest loading the Tetris game onto your Hackvision as a first step. It is on the games page
, and requires particular libraries which are downloadable there. Installing the libraries, compiling the Tetris game and uploading to your Hackvision will give you a good sense for the process. Then you could switch back to Space Invaders/Pong by downloading the Hackvision firmware and required libraries. Note that Tetris and Space Invaders/Pong require different versions of the TVout library.
Good luck and have fun!