For me gameplay (in video games) is specified by the controls, the interface, the virtual environment and how the actual game engine/models and textures work together to make the actual game. It varies with each game, some gameplay can be really tedious where its hard to control the characters or if there is use of a "game camera" that follows the player that doesn't work brilliantly. I think "good" game play depends on the person playing it, people have preferences for how things are done. Its strange that i have mentioned video games first subconsciously but there is of course all the older traditional methods of gaming with cards etc. Another thing that can be added to the list is also the rules of the game.
I dont think there are any major "leading lights" in game design, there are many genres in games now and there are many players who buy different sorts of games, I dont believe that there can actually be a "Best" games design company. There are certainly a lot of them, especially in America and Japan who all do different sorts of games. I dont even have a particular preference to a company.
Typically people would say that all games design happens in an office full of people who are allergic to sunlight or what ever nonsense, it may have been the case with the early games like Pong but I think that in this modern world, especially now it takes more creativity (unless your doing Programming) where you need to go out and research things that are true to life. To be in an office all the time just leads to a lot of stagnation in games design.
Its just impossible for 1 single person to work or lead a commercial game, there are so many sections of it for 1 single person to take all the responsibility for. These different genres that I mentioned earlier would need different design principals, no genres of games are exactly similar and yes different gameplay would be involved and need to be considered.
When im playing the main thing I look for is the gameplay over the other technical parts such as graphics, just how it works, and if the controls and other sections are logical.