By qualify, I took that is 'we won't deport you if you keep your nose clean' But not permanent. They can get to the back of the line and apply, but the status I see he's granting is temporary and conditional. That to me at least isn't legalization, just a reprieve. I realize others may see it differently.
Having myself been a recipient of Legal Permanent Resident status, I can tell you, from personal experience that there is nothing as close to citizenship as LPR status.
So, LPR grants an illegal alien legal status, which is legalization, which is what Cruz said he'd never supported.