But as you say, the author isn't standing up for these "sciences" (in scare-quotes). Rather, he takes issue with the claims of objectivity and rigour for certain fields, one of which you appear to feel is unfairly tarred. You don't need to mischaracterise the author's position to defend computational linguistics though.
He actually says "I do not believe in the primacy of the scientific method as a source of knowledge", and later, that [in order to successfully advance a particular scientific field] we need to "admit the presence and value of non-scientific knowledge". The nature of this non-scientific knowledge is not entirely clear from the essay but seems to be some mixture of culture and common sense.
He throws out several such claims without addressing the problems that come along with accepting non-quantifiable or non-scientific knowledge into a traditionally scientific discipline. For example, if you make a hypothesis that is not quantifiable, how can you determine the degree to which your data supports it?
On a more substantive point: You acknowledge the difficulties faced by "soft sciences". Does that mean you accept that there are whole categories of real-world phenomena of which it would be extremely difficult if not impossible to systematise whatever "knowledge" we do have? I don't think that position is incompatible with respect for science.
Take psychology as an example. The history of psychology until c. 1950 consists of different gurus with different opinions, and since few theories offered testable predictions, no one could be proven* wrong. Psychology has since learned to do controlled experiments and has been more successful. Computational neuroscience and cognitive science are more successful still. Literary criticism, OTOH, is still caught in this trap.
Ultimately, my issue with the author is that he strongly channels Thomas Kuhn. Yes, the political and social contexts of science are important. But they are nowhere near as important as the actual data and arguments made within the scientific framework.
* With all due qualifications about the impossibility of true falsification