I would ask questions, rather than expressing opinions or asking him to do things.
How is the job-hunting going?
How many did you apply for this week?
I'm going to the post box, do you have any application forms to go?
So, when you move into your own place, are you happy to support him long term?
How does he feel about not having a job?
Does he feel guilty allowing everyone else to work while he games?
Will he be happy for you to continue working to support both of you after you move out?
Could he claim jobseekers allowance?
Just keep going, especially with the questions that make her think about his priorities.
Not hearing a word said against him doesn't mean she won't be thinking about it after the conversation has ended.