Find product of the oxidation of 2-methylnaphthalene with chromium trioxide
Fun fact: this synthesis is/was the commercial method used by BASF to make the product, menadione, which is often found as a supplement in animal feeds (patent DE092952709). Apparently the use of stoichiometric chromium is worth it.

Why are alpha positions more reactive? There are two potential questions here, I'll try to answer both. 

1) Why does methylnaphthalene react differently from toluene?
The naphthalene ring is generally more reactive than benzene because reaction intermediates do not fully destroy aromaticity (see below image, left)

2) Why is the alpha position more reactive than the methyl group? 
This question of reactivity is tricky because other oxidants and reaction conditions will indeed oxidize 2-methylnaphthalene into 2-naphthoic acid. In general, electron-rich naphthalenes are able to oxidize into naphthoquinones, even just by exposure to $\ce{O2}$. If we assume (big assumption!!!) that these reactions to go through radical mechanisms, then we are either oxidizing the naphthalene pi system (left) or abstracting an H* (right). There's various arguments to be made about which pathway is more stable based on the extent of conjugation, and obviously that will depend on the reagent and solvents in use as well.



Alpha positions of which functional group have they mentioned?

The alpha nomenclature they use here is actually referring to the two different positions in naphthalene: