Why is phosphorous pentoxide a dehydrating agent?
First of all, your reaction is wrong. $\ce{HPO3}$ does not exist as a single entity. It is actually a cylic molecule of formula $\ce{(HPO3)_n}$. The simplest such compound is $\ce{(HPO3)3}$ which is called trimetaphosphoric acid. See this answer for more details.

So, what happens is that phosphorus pentoxide is very powerful dehydrating agent and can rip off water molecules from compounds. Phosphorus pentoxide can dehydrate nitric acid to form its anhydride, dinitrogen pentoxide.
$$\ce{2HNO3 -&gt;[P2O5][- H2O] N2O5}$$

Why dinitrogen pentoxide is not used as a dehydrating agent?

My take on this is that hydrolysis of dinitrogen pentoxide is not that exothermic as compared to hydroysis of phosphorus pentoxide. Hydrolysis of phosphorus pentoxide is very exothermic, releasing so much energy to dehydrate compounds to form corresponding anhydrides and phosphoric acid.
$$\ce{P4O10 + 6 H2O → 4 H3PO4   (–177 kJ)}$$
Phosphoric acid is hygroscopic which further sucks remaining water from compound. If we compare all the dehydrating agents, phosphorus pentoxide will be on a different league. Dinitrogen pentoxide is nothing.
Nitric acid also hydrolyses to form nitric acid but the reaction is not that exothermic. Also, nitric acid is not that hygroscopic as compared to phosphoric acid for which it is not that great of a dehydrating agent. But hydrolysis of dinitrogen pentoxide has its importance. A solution of dinitrogen pentoxide and nitric acid is a good nitrating agent and hence $\ce{N2O5}$ is known as a nitrating agent than a dehydrating agent. Also, this hydrolysis reaction is a basis of forming atmospheric aerosols ($\ce{HNO3}$ is a good $\ce{NO_x}$ reservoir).