The big question: are there any shipped games (ex. on Steam) with it?

This is probably the most important thing when advertising your game engine. Tech demos (like Arkanoid) are easy to make with any engine, but actual games less so. Even modest indie game releases can include tons of assets and scripting, complex workflows and custom tooling (depending on the game and the team structure), and all kinds of platform-specific tweaks.

Developing a full-blown game often exposes the actual glaring problems of the game engine. And I think dogfooding is incredibly important in fixing these issues (developing a full game alongside with a game engine).