"I apologize to those who were genuinely hurt or offended by the make-up I wore or the words I spoke".
"The make-up I wore" -- he means his repeated use of blackface that most people have known to be quite racist for a long time. He will not use the term "blackface".
"The words I spoke". He means the N word. A tape has surfaced in which left-wing comedian Jimmy Kimmel, was caught using racial slurs on tape. Kimmel used racial slurs while imitating rapper Snoop Dogg’s voice. In the clip, Kimmel uses the “N-word” several times.
He "apologizes" to those who were "genuinely" hurt or offended. Two points here. He is implying some are not genuine in being hurt by him. And that maybe some of those who were genuine are being too sensitive. He does not admit his actions and words were wrong at any time in his statement.
He then goes on to say: "...it is frustrating that these thoughtless moments have become a weapon used to diminish of social and other injustice.". See. He is the good guy fighting for what is right. And it is he who is the victim.
Kimmel then took time away, saying he wanted to spend time with his family this summer. When called on it, he doubled down on his victim-hood, he hid behind his son's rare medical condition -- a rare heart defect. His son is three years old. As far as I know Kimmel did not take last summer off to spend time with his family.