Did you not read the entire second half of the letter?
The thing briefly mentions US foreign policy in the opening, but then goes on to be all about how Islam is the only way and everyone needs to convert to it or the bombings and terror will continue.
And in that section, as examples of the US’s moral failings in the eyes of Islam he cites things like homosexuality as what needs to stop.
So yes, he did hate the US for its freedoms, and at the core of the issue was not simply blowback but religious zealotry.
The US has meddled worldwide. You don’t see South Americans whose democratic governments were overthrown by tyrants who tortured their family members with US support suddenly bombing civilians in the US.
The key difference between the many places the US has pulled some major BS and Al Queda is that only the latter was fueled by religious orthodoxy committed to worldwide forced conversion which then used US foreign policy as rationalization for killing civilians to demand that conversion.
As terrible as terrorist organizations are to the West, they perform exponentially more terror in their own regions in the service of religious conservatism at the end of a sword (literally).
9/11 was connected to blow back for US policy, but it happened because of people who think a religion by a 54 year old who married a six year old should be followed by the entire world and anyone who refuses must die terribly as a caution to the next person given a choice between conversion or terror.