d-Menthol vs dl-menthol: Does an enantiomer and its racemic mixture have different melting points?
If solid menthol were just amorphous, then you would expect the racemate and each enantiomer to exhibit identical melting points. However, if you read further on the Wikipedia page you reference, you'll see that racemic vs. enantiopure menthol crystallizes differently:


  The two crystal forms for racemic menthol have melting points of 28 °C and 38 °C. Pure (−)-menthol has four crystal forms, of which the most stable is the α form, the familiar broad needles.


(This information is trustworthy and corroborated in the primary literature; here is one example)

The melting point of a crystalline solid has to do with how well the molecules can pack together. In other words, on a molecular level, there is an orientation dependence. The better the molecular packing, the stronger the intermolecular forces, and the higher the melting point - since it takes more energy to separate the molecules. This is why the enantiopure menthol has a higher melting point.