Pitcher did not received ER even though 3 should have been earned.

[TreMetal]

nevermind

[zrog2000]

None of the runs are earned since if the error was an out instead, the HR never would have been hit because there would have been 3 outs.

This is one of the ways that ERA is a little dumb since pitching better would have avoided that HR even though there was an extra out in the inning. But in the end, the pitcher who gave up the HR and the pitcher that overcame the error and didn't allow any runs both allowed the same number of earned runs.

[Threnodas]

OOTP is correct here. Earned runs are governed by MLB Rule 9.16, but this Baseball Reference article does a good job explaining it:

https://www.baseball-reference.com/bullpen/Earned_run

The key point from the article is this:

The example shows two general rules of scoring earned and unearned runs:

1. A batter who reaches base on an error can never score an earned run.
2. A run that scores after there should be three outs is never earned.

None of the runs were earned, under point #2 above. Without the error, the inning would have gone like this:

Rickey Henderson: Fly out, F9
Lorenzo Cain: Ground out, 6-3
Matt Carpenter: Base on Balls
Bryce Harper: Fly out, F9
Bottom of the 6th over - 0 runs, 0 hits, 0 errors, 1 left on base; Hamilton 3 - Torrance 0

Even though the offense/pitcher were responsible for all the runs except Cain's ROE, they aren't charged to the pitcher because that inning should have been over. Note: if a reliever is brought into an existing inning, he no longer gets the benefit of the previous errors for ER purposes; his runners are his.