Comparing SN2 reaction rate for phenacyl chloride and methyl chloride
First, let me point out that a rate difference of 500 is really not that large.  There are solvolysis reactions with relative rate differences on the order of $\mathrm{10^{10}}$ or greater (1).

The transition state for an $\mathrm{S_{N}2}$ reaction involves hypercoordinate (or hypervalent) bonding.  The transition state is, more or less, a trigonal bipyramid structure and the bonding at the central carbon atom ($\ce{Nu-C-X}$) involves a 3 center-4 electron bond (see the above link and links therein for more detail on this concept). With 5 electron pairs being shared by this central carbon, anything that removes electron density from the central carbon atom will prove beneficial and accelerate the reaction. 



$\mathrm{S_{N}2}$ Reaction Pathway

In your molecule #2, a benzoyl group is attached to the central carbon involved in the $\mathrm{S_{N}2}$ process.  You are correct that such a group is larger than a hydrogen and should decrease the reaction rate due to steric effects. However the size of the benzoyl group is not exceptionally large and the steric effect will likely be small. More importantly, the benzoyl group will also exert an electronic effect. The central carbon in an $\mathrm{S_{N}2}$ reaction is $\mathrm{sp^2}$ hybridized [e.g. leading to a trigonal bipyramid structure as mentioned above] and has a $\mathrm{p}$ orbital.  This $\mathrm{p}$ orbital can interact with the adjacent carbonyl group through resonance.  This resonance effect will tend to remove (delocalize) electron density from the central carbon atom.  Also, the carbonyl group will inductively remove electron density from the central carbon atom.  These electronic effects will remove electron density from the central carbon atom thereby accelerating the reaction as observed.

(1) For example, the relative rates of solvolysis of 7-tosyloxynorbornane and anti-7-tosyloxynorbornene in acetic acid are $\mathrm{1:10^{11}}$