From the abstract:
Effects were observed regardless of age, gender, baseline magnesium levels, baseline severity of depression, or use of antidepressant treatments. It worked quickly, was well tolerated, and is much safer and less expensive than conventional treatments with medication.
This study found clinically significant results for the use of magnesium to improve both depression and anxiety. More research will hopefully be done in this area, but here is just another good reason to ensure your dietary magnesium uptake is sufficient.