I don't think so. A cop might be able to get away with as they are apparently given more latitude than the average joe when it comes to using lethal force to stop a fleeing felon.
For a "Non" peace officer, you have to have a concern about imminent harm. If the guy is running away, I think that is going to be a hard sell.
http://apps.leg.wa.gov/Rcw/default.aspx?cite=9A.16.040 - Use of force by peace officer
http://apps.leg.wa.gov/Rcw/default.aspx?cite=9A.16.050 - Justifiable homicide by "other" person
I am not so sure I could personally justify possibly taking a life over the theft of my wallet, regardless of what the law might allow.
Of course I am not a lawyer, yada, yada, yada.