Perhaps. Sometimes you have to dig a small hole to find more of the plot.
In Double Impact he/his brother are taking revenge in a not-as-noticable way. With Bloodsport, he joins the tournament to honor is Shidoshi and in Kickboxer he wants revenge on Tong-Po for paralyzing his brother. With Hard Target, tho, he's helping a woman find her father and then solve his death until the bad guys hunt him--then he hunts them. Nowhere to Run involves him helping a (hot) woman with corrupt men who insist on owning her land--even by excessive force. Hell, the film Sudden Death was just Die Hard in a hockey stadium and Timecop involved him trying to stop a corrupt senator from stealing money and killing people thru time travel to control America in hte future.
So really, not all of them are like you think--but it's a common steriotype for him, like Seagal.