I have an idea that his version of liberal would place him somewhat to the right of most of us...
In the Middle East liberal means against the rules of religious leaders.
He is talking about liberalism in terms of islamist dogma and not in political economic terms. In this sense, liberal has nothing to do with left vs right, but rather is a contrast of fundamentalist islamist jihadism vs "moderate" vs theologically liberal. Note his comment about "banning headscarves" at the university. The fundamentalists would require full burqas, the moderates would allow a more moderate form of dress, the "liberal" would go further than simply making the burqa and headcovering optional by banning the headscarves altogether.