Rockhill has moved away from the term "Western left" and switched to "Compatible left." (Its better to not use geographic terms for political tendencies) He uses it more of a description of institutions and schools of thought.
The western/compatible left are happy to engage in liberation theory and critique but not action and not even solidarity of those who take action against imperialism that has a chance of success. They are "as left as they come"... without it being a threat to the status quo.
Both zizek and varoufakis have engaged in imperialist accommodation. It would be more beneficial for people to use that form critique rather than just labeling other people but most internet leftists engaged in "debates" aren't exactly careful with their words.