|clanlib||Cross platform C++ toolkit library. Its primary focus is on games.||2001 / 2012||16 games|
|Flixel||A free, open-source game-making library for Actionscript 3 and designed for use with free development tools.||2009 / 2014||19 games|
|libgdx Framework||Cross-platform framework for games.||2012 / 2015||17 games|
|Moai||Created using the Moai development framework, a mostly Lua driven cross-platform game development kit created by Zipline Games.||2011 / 2014||9 games|
|Nvidia GameWorks||A toolkit and collection of APIs for game development from Nvidia.||2012 / 2016||12 games|
|pygame||A game development framework that wraps SDL for Python.||2001 / 2017||163 games|
|XNA Framework||Made with and uses the XNA framework by Microsoft, a set of tools and a runtime for game development. Or the Mono.XNA open-source and cross-platform re-implementations of the API.||2008 / 2017||74 games|
Libraries that contain large number of functionality one would need to make a game, and are there specifically for that purpose (including functionality that presumably only games need), but is not and does not have an engine on itself.
Alternate name: Game frameworks
Many sources seem to consider game engines and game libraries the same thing even though game libraries require much more technical work to get a game running on. This is also exacerbated by game libraries that partially cross over to game engine zone but don't fully go there (e.g. Moai).