Engines have improved on the closed formation front in the last years. Still there is certain individual positions that favours humans yet.
Playing the stonewall system don't seem to work anymore unfortunately.
On your question: in closed pawn chains the engine will in general just shuffle the pieces back and forth, mainly because they won't risk to harm the stability of the pieces. So a random King move can mean such behavior.
I heard from my chess class that computers are best at tacitcs. But what will it do in closed positions, where there are rarely any opportunities?