Many get a cathartic release from seeing their posts displayed.

yelp listed a bunch of businesses in my area and a staffer came around and wrote reviews for all of them ... so they were getting paid to write them.

Yelp - What Motivates Their Writers?

In some cases it could be free steaks [latimesblogs.latimes.com], but according to a recent news article, money is the motivation, as little as five dollars [reuters.com].

There are plenty of reasons why a person have to make a long and detailed reviews on Yelp. It can be that he/she is too overwhelmed by the service and value he/she got form dining from that particular restaurant, they may be advised to to so by the one who hired them to make reviews, maybe they are so motivated to write such reviews during that period and the list goes on and on...

I think the OP is asking why they don't do that on the OP's site, asking what is it about Yelp that makes people longwinded?

Exactly, MB. I'm comparing the very same restaurants, clubs and hotels on my site that the Yelpers are writing about today, yet the (non-paid) reviews I received on my site were generally much shorter and far less detailed.

Though there are people who sincerely just want to get their opinions out there, behind most of those long, elaborate reviews these days is money...somewhere.

Reputation management
Publicity
Affiliate earnings
Write for hire
Rewards
Bribery
Nepotism
Competitive sabotage
Add any assorted known bias-producing substances...

The revised FTC guidelines only touched the surface of how reviewers get compensated in the new economy.

Can anyone explain to me WHY people on Yelp write such long, detailed reviews if they're not getting paid to do so?

who says they are not getting paid? Anyone can hire one for a few bucks to write about anything.

Yeah, I saw a news story years ago, that said at least in the travel industry.. the majority of reviews were paid for.

Money

TripAdvisor investigated by Advertising Standards Authority after complaints [telegraph.co.uk...]
I think the public / industry is probably savvy enough to spot the authenticity and quality of reviews.

Up until recently I believed the tripadvisor reviews. Now I do not read them because I do not trust what is written on them. I stopped believing Yelp reviews a few years ago after several fake reviews led me to some really poor restaurants.

I think most people believe the reviews on tripadvisor, amazon, yelp and others. Recent articles about the industry leave me with the impression that the steps they are taking to catch fake reviews are inadequate.

Getting back to the OP, perhaps a way to encourage a longer review is to install a script that counts the words and nudges reviewers to post more. The alternative is to rank exceptionally well for specific phrases that make it worthwhile for those vested in the reviews to leave long reviews, whether it's a disgruntled customer or a business owner.

I think most people believe the reviews on tripadvisor, amazon, yelp and others

...until they experience what you have, and then the brand experience starts to suffer.