He isn't blaming science, he didn't say "Stop teaching science because the Order of Science is amassing its minions and spreading its agenda."
He used science to show that humans are going to destroy the planet.
He used nuclear war and global warming as proof of this. Yes these are technically both results of advancing technology due to scientific progress, but they are more due to the attitude of human beings towards this planet.
Hawking also explicitly blamed the "careless hubris of the ruling elites and their tendency to act in favor of profit". Here he is talking about the corporate fat-cats that will slap 'eco-friendly' on a package despite that fact that it's been flown in from China, where it was made by 8 year old orphans.
If you think of Science as a tool, he didn't blame the tool: he blamed the people using them. For example, you wouldn't blame a hammer for knocking a hole in your wall, you would blame the person who swung it. A lot of scientists (like Stephen Hawking) are theoretical scientists. That means that they discover new things, they do not get to decide how their discoveries are used.
I think that Stephen feels as though once upon a time science used to be purely about knowledge and advancing quality of life, but now huge corporations will pay a team of researchers more money than the opposition to not publish data. Instead of being for the benefit of the whole of mankind, scientific advancements are being used primarily by the highest bidder.
You can't blame science for this. You can't blame scientists for this. You have to blame the people who sit on top of the ladder and do everything in their power tot make sure that the system never changes.