I don't think there's an exact definition of the term, and views will vary.

I'd agree with Jerry on the "short repeated motif, often used in the introduction" view but not the "of no direct relation to the melody line" aspect. Many riffs are the initial melody line.

Personally, I think the guitar line in "Parisienne Walkways" is too long to be described as a riff. I'd probably call it a 'theme'.

Dave, you may find this BBC Four documentary from 2014 of interest. It contains numerous thoughts on the meaning:

The Joy of the Guitar Riff