A language written just for writing games is going to be a scripting language within an existing game engine.
and if such an engine didn't exist, what features would you like to see in the language that you used to implement the required custom engine?
obviously, if you're building a game for which a perfectly suitable engine exists, there's no need for a "game programming language".
A language suitable for engines isn't necessarily suitable for game logic, it is two fairly different beasts.
For engine level code you want fairly low level functionality, good control over memory layout and access, keywords to provide optimization hints for the compiler (pure/impure functions, hot/cold functions, memory aliasing information, etc), support for SIMD in a way that works well across different CPU architectures and doesn't fail miserably on platforms without SIMD support and ofcourse easy access to existing C and C++ libraries (as most current systems have C APIs)