Just to be clear, here's the rule on RBI:
10.04 RUNS BATTED IN
A run batted in is a statistic credited to a batter whose action at bat causes one or more runs to score, as set forth in this Rule 10.04.
(a) The official scorer shall credit the batter with a run batted in for every run that scores
(1) unaided by an error and as part of a play begun by the batter’s safe hit (including the batter’s home run), sacrifice bunt, sacrifice fly, infield out or fielder’s choice...
Because the runs here scored solely as a result of a throwing error, the batter is not credited with any RBI (btw, if the runner had been entitled to reach base as a result of a dropped third strike, he still wouldn't have been credited with any RBI if the runs had scored).