Why is boiling point of Ammonia greater than Arsine?
There is the general trend in the groups 15, 16, 17 of raising of boiling points for the binary compounds with hydrogen, going down the groups.
But the first members of each group - $\ce{NH3, H2O, HF}$ - have anomally with their boiling points being exceptionally high, due hydrogen bonds. The strength of these bonds and the boiling point decreases in the order $\ce{H2O &gt; HF &gt; NH3}$.
See the figure 2 on wordpress page for an illustrative picture:

Hydrogen bonds play role in (not limited to):

evaporation and boiling, as molecules need to gain an extra energy to overcome these bonds and to escape liquid.
condensation, acting as cohesive force for molecules to stick to each other or to a condensation center.
gas pressure, as the inter-molecular cohesive force decreases the gas pressure, compared to the pressure of an ideal gas at the same conditions.

Note that the fact that both NH3 and AsH3 are gases at room temperature is irrelevant for the above.