"Normal" home runs are those that leave the park, that fielders don't have a chance of catching. As a result, they are not counted in the "balls in play" part of BABIP.
On the other hand, an "inside the park home run" is a hit that remained in the field, was presumably "fieldable," and just happened to go for four bases. Would it be excluded from the "balls in play" part of the BABIP calculation like the other kind of home run?