Since launching K'nex, the idea that none of the big players (including Lego) wanted, back in 1992, he has seen his business grow from $1.5m to $100m, with the result that he claims Lego's once seemingly impregnable position has been substantially weakened.
His product - which allows children of a variety of ages to make models of everything from butterflies and dinosaurs to lorries and ferris wheels by linking plastic pipes and connectors - has rapidly gained about a quarter of the British construction toy market and similar proportions of others around the world.
Moreover, now they have seen the concept in action, some of the leading manufacturers have changed their tune. Hasbro has formed a joint venture with Mr Glickman, together with his brother Bob, to market the product around the world, while Lego has just launched a product called Znap that the Glickmans believe is a similar concept.
There is an apocryphal tale of how it all began. It tells how in 1988 Joel was at a wedding and started fiddling with the plastic straws in his drinks. Connecting them together and making geometric shapes, he saw the idea for a toy.
In fact, he now says, it was not quite like that. "That's just the soundbite," he claims, adding that he and his brother had already decided that their Philadelphia plastic components factory had limited growth opportunities.
They were looking around at various sectors and decided on toys because Joel thought that he could design one, and, moreover, the business could make the parts.
So, while it was true that he spent the wedding playing with straws he did not come up with an instant success. "It didn't work worth a damn," he says.
But it did sow the germ of an idea that led him to develop something that intrigued people. "I felt like the Pied Piper with K'nex," he says. "Kids would follow me around."
As a result, he duly approached the major manufacturers. "I felt my job was complete. What I wanted was a manufacturing contract and a royalty and I'd get on with improving my golf handicap," Mr Glickman adds.
But it was not to be. They sent rejection letters that are now pinned on Joel's wall. But he was sufficiently convinced he was on to something that he decided to go about making it himself on the basis that if the people already in the toy business were dumb enough not to see the potential, the industry could not be that difficult to learn.
A break that led to an entry at his local Toys 'R' Us produced his first sales - at Christmas 1992. When an astounding success in the Philadelphia area was followed by a national roll-out that saw sales shoot to $20m, the big companies, particularly Mattel and Hasbro, came calling.
In the event, he and his family selected Hasbro as the joint venture partner largely because of the personalities of the executives involved. In particular, Norman Walker, then president of Hasbro International, recommended that they bring in Peter Brown, an Englishman who at the time was European managing director of rival toy company, TOMY, to develop the business.
Mr Brown says now that he happily abandoned his secure position to join a three-man team because of "Joel's enthusiasm for the product, and his belief in it".
Meanwhile, Mr Glickman - who was in London last week for the launch at the Science Museum of the latest version, said to be the world's first solar-powered toy - replies that Mr Brown and other recruits have brought a whole range of new facets to his original idea.
But the British connection does not end there. The toys, which have won numerous awards and are acclaimed for their educational value, are put together at a plant at Ashford in Kent from components made at the Glickmans' factory, ready for shipment to more than 40 countries all around the world.
Mr Glickman and his brother still run their plastics factory, but are content to leave packaging and distribution to the team on this side of the water. "That's kind of my management style," says Joel, adding that the business is run "by remote control".
Moreover, the American side of the business is now headed up by Mr Walker, the former Hasbro executive whose empathy attracted Mr Glickman to the joint venture deal four years ago.
In fact, were it not for his irritation with Lego over Znap, he would be highly contented with life. Pointing out that the Danish company was among those who claimed the K'nex idea would be a flash in the pan, he says: "I'm damn angry about it. I could design a better brick than the Lego brick, and I just may well do that."
A spokesman for Lego UK says Znap is "nothing like K'nex" and is fully compatible with existing Lego products.
Mr Glickman adds philosophically that, "ultimately the kids and their parents will decide". To judge from the crowds that have appeared at the Science Museum, Lego could have a real fight on its hands.