According to the (4 year old) article there are no clinical studies showing that the gut microbiome analysis might be useful for either explaining or treating a chronic inflammation.
That is pretty far from it being considered "alternative medicine"
In my opinion there being no evidence in either direction does not mean that you should not try it, especially if there is no downside and you have a chronic condition.
I assumed lack of evidence + non mainstream opinion = alternative medicine. Maybe there is a better word for cases like this where there is some evidence but no clear indication of causality.
We know that a diverse microbiome might be healthier than a non-diverse one. Exercise, eat your fibers, legumes, fruit and whole grains. Avoid processed food. Enjoy some fermented condiments. Avoid alcohol.