It still targets the ACE2 receptors found throughout different human tissue, and reportedly can bind even more effectively to it. The difference in severity is reportedly because it replicates 70x faster in the bronchus but 10x slower in the lung tissue, leading to more bronchitis and upper respiratory involvement and less pneumonia.
I wouldn't be surprised if there's lower incidence of chronic complications than Delta and earlier variants, though. Long COVID seems to be associated with (but not unique to) more severe cases. If there's pneumonia or ARDS, there's a much easier pathway into the bloodstream than if it infects mucus membrane tissue in the upper airways. It likely can still cause long COVID, but at a lower rate corresponding to its generally lower severity.
Obviously, full studies of long-term effects are lacking, since Omicron has only been out for a month and a half.