Pyramid Scheme? Close. More like the Free Widget Scheme.
You don't see any money directly, but rather each person you enlist pays [indirectly] the company running the scheme in the form of a "referrer fee". If you convince enough people to sign up, you get the payoff in the form of a "free" widget.
The classic "pyramid scheme" is illegal because it is deceptively fraudulent, not because "it doesn't work". Pyramid schemes work marvelously for early investors even though most people end up losing money,but it's sold to people as a way to make money. Currently the "free iPod" variant isn't illegal but is just as deceptive.
Even if the company always does exactly what they say they will do, it's still a scam.It's a scam in that most (if not all) of the entrants sincerely believe they're eventually going to receive a free gadget yet the vast majority of them will not. If 5 people are required to sign up before you can get a free widget, at most 20% of the people who join may eventually receive one. Of course, the percentages are even lower for those items requiring more referrers. And, as time goes on the chances of success shrink drastically as the number of potential new members goes down.