Fake. The same guy ("TrolleyRulle") trolled people on Reddit just after the 2013 Boston marathon bombings. He posted a link to book/manifesto allegedly written by Dzokhar before the attack, which turned out to be fake. He used the same words ("mind rape" etc.) in this "book".
Youtube video about TrolleyRulle as Adam Lanza is from 11 years ago and these claims were quickly debunked on forums. Same with alleged Lanza's 4chan posts etc.
TrolleyRulle guy was known for pretending to be various attackers from 2012-2013 and trolling other people on Reddit and YT.