Gameplay is the term given to the tactical aspect of a computer game, such as it’s plot and the way the game is played, as distinct as the graphics and sound effects part of the video game. Gameplay is a massive part to any game. If the gameplay sucks, the game sucks. End of.
Art direction in games also plays a huge part. If a game like Gears of War had a completely different art direction, I’m going way out here, and the colour palette was full of saturated oranges and pinks, the game would have a completely different feel.
I think computer games differ a lot from board games, unless you play Monopoly on the PC. But the whole feel of a computer game is different. Board games are what they are. You can argue that Monopoly is one of the best board games ever created; but given the choice; a thirteen year old would rather blow a virtual terrorists head off, than buy Mayfair.
The typical way to approach the design process is to start from a previously completed concept and create a game design document from that. The development team uses this document in order to map out the game design. This is updated as the game progresses through the development process.