What do you call "intellectual" jobs?
How about white-collar?
From M-W:
white-collar: of, relating to, or having the kind of jobs that are done in an office instead of a factory, warehouse, etc.
You can call these people who rely on thinking in their jobs knowledge workers doing knowledge work. They 'think for a living' and need to solve non-routine problems.
These are generally referred to in the UK as professional jobs.
professional
- engaged in one of the learned professions : A lawyer is a professional person.
The antonym, for physical jobs, is manual jobs.
Knowledge work is sometimes found as a back-formation of the much more common "knowledge worker".
You could also say a profession that is part of the tertiary industry, meaning everything that's service related.