My 2 cents: "Alternative medicine" encompasses all the approaches to healthcare that outright ignore (partially or completely) what is scientifically established regarding how our bodies work, and present their own, alternative approach to explaining our bodily functions, and the relevant problems.

Therefore, no, diet-related approaches do not qualify as alternative medicine. It is well known that our diet has a significant influence on our general health, it is what one would call the "mainstream opinion" on healthcare, not an alternative one. The fact that certain medics prefer to treat the consequences with no regard to the potential dietary causes of the problem is a separate issue.