A couple of minimalistic (as I understand the term, it may not be entirely accurate) games are Daniel Benmergui's I Wish I Were The Moon and Sam Barlow's Aisle.

IWIWTM relies on a simple one-click interface to produce widely different effects in the game world. It has taken a point-and-click design and stripped it of all trappings of inventory, puzzles, story or dialogue. Instead the gameplay is in finding what can be done with the snap-shot interface.

Aisle is a one-action interactive fiction piece in which your one act produces widely different results. The text itself is complex but if you imagine the scenario to be presented on a stage it would certainly appear minimal.

The minimalist approach, and analysis through a minimalist perspective, can lead to less cluttered and more immediately accessible games. RPGs, shooters, RTSs, all the classic genres are now mired in decades of accumulated complexities as developers strived to do something new and different and 'better'. Games like Portal, which strips the shooting from a shooter and largely relies upon the navigation and platforming elements of the modern first-person game, have shown that a simple game can enthral and excite players while being commercially viable.

I believe there is a growing segment of 'gamers' and games enthusiasts who are tired of superficially complexity. By looking at the underlying framework of modern games, developers can take the mechanisms on a different evolutionary path to the one followed over the past 20, 30 years and arrive at something fresh and engaging.