a spiritual outlet
is some place which would be considered to be good for one's spirit or soul, where one can feel free from the grind of day-to-day living.
The author is saying rivers allow one's inner feelings (one's spirit or soul) to feel peaceful, calm, soothed, meditative, and "at one with nature".
Rivers can be very beautiful with calming white noise from shallow water running over rocks and boulders. A cooling respite in the summer from the heat of the concrete jungle.
If you've ever seen the movie A River Runs Through It, it is a beautiful illustration of fly fishing in Montana and how meditative it can be.