Halogenation of an alpha-halogen ketone in acidic conditions
The same mechanism discussed in my answer to your earlier question on acid catalyzed halogenation alpha to a carbonyl still applies here.  For reference, here is the same link supplied earlier that shows the mechanism for this acid catalyzed halogenation.

In that earlier answer I said that the enol that "produces the more stable double bond (the one that is more highly substituted)" is the enol that will form and react nucleophilically with the halogen to produce the alpha-halo carbonyl product.  In light of your new question, the statement that more highly substituted double bonds are more stable needs some qualification. 

The closer in electronegativity a substituent is to carbon, the more it will stabilize a double bond.  Consequently, the more alkyl groups attached to a double bond, the more stable the double bond (barring large steric effects).  On the other hand, fluorine destabilizes a double bond.  It is so electronegative that it prefers to bond with orbitals high in p character.  When forced to bond to a double bond $\ce{sp^2}$ orbital (that is enriched in s character) destabilization results (see this earlier fluorobullvalene example for more on why fluorine "hates" to be on a double bond).

Based on its electronegativity, chlorine should be somewhere between fluorine and an alkyl group in terms of its ability to stabilize a double bond.  If we compare the heats of formation of 1-butene (-0.1 kJ/mol) and trans-2-butene (-11.2 kJ/mol) we see that placing the methyl group on the double bond stabilizes the molecule by 11.1 kJ/mol.  If we compare the heats of formation of allyl chloride (-5.6 kJ/mol) and trans-1-chloropropene (-12 kJ/mol) we see that the placing the chlorine group on the double bond stabilizes the molecule less, only 6.4 kJ/mol.

These differences mean that we will have much more of the enol without the chlorine on the enol double bond, then we would have of the enol without the methyl group on the enol double bond.  So we have more of the unsubstituted enol in the chlorine case and the enol with the chlorine on the double bond is much less nucleophilic (less reactive) due to the electron withdrawing inductive effect of the chlorine substituent.  These two factors combine to make the second alpha-chlorination take place on the unsubstituted side of the molecule.

As to steric effects, they probably don't play a significant role.  One metric commonly used to compare "steric size" is the cyclohexane A value.  The A value for chlorine is 0.43, much smaller than the A value for methyl (1.7), suggesting that a chlorine substituent is smaller than methyl substituent.