In the OES_texture_cube_map, a new GL_STR symbol and the GL_TEXTURE_GEN_STR symbol in OpenGL without are
defined.

The value of these symbols is uncertain.
To which document have you been described?

An initial value of GL_TEXTURE_GEN_MODE is GL_EYE_LINEAR in OpenGL.
However, GL_EYE_LINEAR is outside the support in OpenGL ES.
Then, what is an initial value of GL_TEXTURE_GEN_MODE of OpenGL ES?