I wonder if there are any game engine written in Scala or easily accesible from Scala?
All the Java gaming engines are easily accessible due to easy Java integration. There are several (not sorted in any way):
A good presentation how to start coding a game in Java is Write a 3-D Game in the Java Programming Language in Less Than 50 Minutes that applies as well.
As Scala has a nice Java integration the ointerop should be easy. As mcherm pointed out, for lwjgl this has already been done. To have the nice Scala feel you could add some implicit conversions.