If we look at its mirror image about a mirror which is perpendicular to plane of the molecule, the two \ce{-CH3} groups which are pointing upwards and downwards (implied by the wedge and the dash) will interchange their positions:

But also the mirror image would be perfectly superimposable on 1,2-dimethylcyclobutane. Hence, it should be achiral, but the answer key says it is chiral. Is this compound an exception?