Can this happen in secondary property markets?
No - the sale of a property in the secondary market is for a fixed physical asset - all the fancy bookwork in the world won't make it happen that I have two bidders for my property, and somehow the price I get for it is the sum of A and B's offers. For Ponzi to work in this situation, that is what would have had to happen.
Wrong. And your explanation goes down hill after that. What you have posted is a salesman's excuse why secondary property bubbles are not a Ponzi scheme, it does however explain why property CAN be a PONZI scheme but attempts to suggest that 'secondary' property is different from other property, thet because its an asset, its has a 'fixed' value. Ponzi schemes are not about adding assets or whatever crap its trying to put forward as an excuse.
Ponzi did not sell real assets in any case, he sold stamps.
Ponzi schemes are about conning people into believing that returns on investments will be ever increasing and those returns are paid for by later entries to the scheme.
Lets take Wikipedia's explanation
"A Ponzi scheme is a fraudulent investment operation that pays returns to separate investors, not from any actual profit earned by the organization, but from their own money or money paid by subsequent investors. "(Property - Check)
"The Ponzi scheme usually entices new investors by offering returns other investments cannot guarantee (Property - Check)
"in the form of short-term returns that are either abnormally high or unusually consistent."(Property - Check)
"The perpetuation of the returns that a Ponzi scheme advertises and pays requires an ever-increasing flow of money from investors to keep the scheme going."(Property - Check)
"The system is destined to collapse because the earnings, if any, are less than the payments to investors. Usually, the scheme is interrupted by legal authorities before it collapses because a Ponzi scheme is suspected or because the promoter is selling unregistered securities. As more investors become involved, the likelihood of the scheme coming to the attention of authorities increases. While the system eventually will collapse under its own weight, " (Property - Check. In that situation, as it a legally allowed scheme, the crash happens when the world runs out of money)
"Knowingly entering a Ponzi scheme, even at the last round of the scheme, can be rational economically if there is a reasonable expectation that government or other person or organisation will bail out those participating in the scheme."(Property - Check)
So, yes, the property market is a Ponzi scheme. A nice, legal, safe, predictable one but with the same end result - the suckers who bought at the end get shafted.