Design this...

Gameplay falls under a few categories in my opinion, it essentially relates to the players control in the game including a load of aspects like freedom, the control system and the players relation to the narrative of the game. I think over the years the idea of gameplay has changed as much as the idea of game design, probably because they're quintessentially the same thing. If gameplay is the users experience within the parameters of the game then the design of the game is entirely responsible for this.
Games design used to be entirely up to the programmers, who were struggling to make something fun out of the limited hardware they had available. As technology progressed the walls of limitation that programmers faced began to disappear and as the game industry grew consumers were wanting more. This is the point where it began to be necessary for companies to employ games designers. Games designers are specifically employed to come up with ideas for the games company. A good, well functioning game with a decent narrative is what people were after, it was up to the designer to visualize these aspects withing the game.
In the beginning focus was laid heavily on level design, as this is where everything takes place and where most of the atmosphere comes from. Now thought is put into all areas of the game and its design is very much like crafting a story, its much like any other media; set design, script writing, projection of characters are all equally important in games.
I'd say that games design is a responsibility of the whole development crew, if a game is lacking in one area, it can ruin the overall experience, if the game has a crap plot you feel no real reason to carry on with the storyline and if the character is an irritating tit you feel nothing when controlling him, wanting nothing to do with the prick. Also the designer or design team need to know enough to carry a solid environment for a decent experience, I think that yes; the design of a game should be related to the theme of it, inconsistency is a constant annoyance to gamers. Personally, storyline is a huge element of my gameplay, I said in an earlier book that playing a game should be like reading a good book, this is fundamentally true with every aspect of the game, also a flexible control system is always a bonus.