It also depends on the type of game and how well sync'd it is with the monitor refresh. There's something undeniably buttery smooth about a solid vsync'd frame rate equivalent to your monitor's frame rate, which just isn't present at lower frame rates. Smooth inputs result in slick oily outputs. And there's less lag between input and output as the frame time is smaller, while game loops are normally sync'd to the frame rate, so a higher frame rate will result in less lag between input and display.

I would also make the point that this is (to me) most visible in PC games controlled with the mouse, especially twitch-sensitive FPSes. Your link relates to console games, which need only cope with the relatively blunt instrument of a controller, and output to what's likely to be a relatively slow display. Most purists would agree that first-person shooters work best with a mouse and keyboard, rather than an analogue controller. And by slow display, I don't mean the refresh rate, but rather the combination of response rate and frame lag.