The "time between innings" averaged 42:41. This is time to watch the scoreboard, watch the silly on-field contest (particularly at minor league parks), visit the refreshment stand or the bathroom, or both. On TV this is simply commercial time.
By far the most time-consuming period of inaction is the "time between pitches." This took up an average of 1:14:49. That's not all that far from half the WSJ analysis's average game time of 2:58. Technically, the time between pitches begins when the pitch to the batter who saw the last pitch concludes—either when the catcher catches the ball or it is fouled off—and ends when the pitcher begins his next pitch. So it includes the unstrapping and re-strapping the batting gloves, sleeve adjusting, helmet adjusting, practice swings, plus the pitcher doing whatever it is he does as well.