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I disagree with your assertion that DOT_SAGE is the only valid variable listed here. All but one of the listed variables are still valid, most used by either local/bin/sage-env or by src/sage/env.py:

• DOT_SAGE: yes, see both sage-env and env.py
• SAGE_RC_FILE: yes, see sage-env
• SAGE_STARTUP_FILE: yes, see both sage-env and env.py
• SAGE_SERVER: yes, but only used when downloading packages: see build/sage_bootstrap/mirror_list.py.
• SAGE_PATH: yes, see sage-env
• SAGE_BROWSER: yes, see src/misc/viewer.py; I think it also gets used by the old Sage notebook
• SAGE_ORIG_LD_LIBRARY_PATH_SET, SAGE_ORIG_DYLD_LIBRARY_PATH_SET: yes, see src/repl/interpreter.py.
• SAGE_CBLAS: I'm not sure about this one; it may not be valid anymore.

See also http://doc.sagemath.org/html/en/installation/source.html#environment-variables for environment variables used when compiling Sage.