It's a very uncharitable definition, sure.
There's no organisation, recruiting, directors, membership or promise of payments.
But those definitely exist, just not via any singular organization. There very much is organization and organizations, recruiting, would be directors, unofficial membership in the club of ownership, and lots of promises of payments.
When people make that comparison, what they're really saying is Bitcoin is mostly funny money which above all else has enriched early adopters and will probably lose a lot of late adopters lots of money. It's ceased to even be a useful currency.
You don't have to squint very hard to see the comparison, even if it isn't flattering or technically the same thing as a pyramid scheme. This is from your link:
In a pyramid scheme [Bitcoin], an organization compels individuals who wish to join to make a payment [purchase Bitcoin]. In exchange, the organization promises its new members a share of the money taken from every additional member that they recruit [to the moon]. The directors of the organization (those at the top of the pyramid) also receive a share of these payments. For the directors, the scheme is potentially lucrative—whether or not they do any work, the organization's membership has a strong incentive to continue recruiting and funneling money to the top of the pyramid.
Such organizations seldom involve sales of products or services with value. Without creating any goods or services, the only revenue streams for the scheme are recruiting more members or soliciting more money from current members. The behavior of pyramid schemes follows the mathematics concerning exponential growth quite closely. Each level of the pyramid is much larger than the one before it. For a pyramid scheme to make money for everyone who enrolls in it, it would have to expand indefinitely. This is not possible because the population of Earth is finite. When the scheme inevitably runs out of new recruits, lacking other sources of revenue, it collapses. Because in a geometric series, the biggest terms are at the end, most people will be in the lower levels of the pyramid (and indeed the bottom level is always the biggest single layer).
In a pyramid scheme, people in the upper layers typically profit while people in the lower layers typically lose money. Since at any given time, most of the members in the scheme are at the bottom, most participants in a pyramid scheme will not make any money. In particular, when the scheme collapses, most members will be in the bottom layers and thus will not have any opportunity to profit from the scheme, yet they will have paid to join the scheme. Therefore, a pyramid scheme is characterized by a few people (including the creators of the scheme) making large amounts of money, while most who join the scheme lose money. For this reason, they are considered scams.[2]
Sounds like many cryptocurrencies and Bitcoin is approaching that if it hasn't hit it already.