Here is also a website where you can see if there is an open source port to non-open source games or an alternative that e.g. tries something of its own / based on the gameplay. As an example, the following "clones" are listed for Minecraft: Minetest, Mineclone2 (now VoxeLibre), ManicDigger and more.
Edit: fixed some grammatic fails.
To name a few: AssaultCube, Battle for Wesnoth, Cube2: Sauerbraten, FligthGear, Freeciv, Freeciv21, Nexuiz Classic, OpenArena, OpenHV, OpenRA, OpenTTD, Remnants of the Precursors, SpeeDreams, Stone Kingdom, SuperTux, SuperTuxKart, Unciv, Urban Terror, Veloren, Warozone 2100, Widelands, Xonotic
P.S. It may be that not all of them are FOSS, but they run natively on linux.