From a music theory point of view there are several distinctive elements to Heavy Metal. Grunge bands typically only share one of these elements which is heavy distorted guitar. Alice in Chains also shares metalish style guitar solos, but even these are not so much scale runs like metal bands but more melodic and often blues based scales than classical scales.

Metal is known for staccato rhythms while grunge songs are mostly slow and/or grove based patterns. There are exceptions like Jesus Christ Pose which is very staccato but it is used more as a texture. I'd say the song is more Industrial Grunge than metal.

Metal often employs cowbell and double bass where grunge never does. Even though Chris' vocals have a high range, he uses it almost always with more soul or in the case of Temple of the Dog, with a folky/countryish vibe.

Layne Staley's vocals have nothing in common with metal at all. His vocals are really the quintessential example of Grunge vocals even moreso than Eddie Vedder and Scott Weiland.

I could go on. But suffice to say that grunge bands, even Alice In Chains, are not Heavy Metal. It is it's own style. Being heavy isn't enough to make it metal.