In addition, Winston and Julia feel safe in this room. They often comment that no harm can come to them here. There are no telescreens, no posters of Big Brother, no hidden mircrophones, no rules to obey. They are in a pocket of safety, a pocket of emotional stability and physical connection that is forbidden by the Party. They are meeting in the room above Mr. Charrington's shop in the Proletarian region which is against the law...their relationship and the risks they are taking are their own rebellion against the Party. This is why Winston is so enamored by things of the past--the paperweight, the rhyme about the church bells, the makeup and perfume the Prole women wear, etc.
Symbolically, Winston and Julia's relationship is like the paperweight. It is beautiful, forbidden, fragile, and the coral is protected in the depths of the clear and smooth glass. But, like the paperweight which is smashed by the Party police when they sweep suddenly into the room where Winston and Julia meet, their relationship has been visible all along, and smashed right along with the paperweight itself. In the end, the paperweight is extinct, and so are Winston and Julia...just like the extinct animals in the quote.
What this quote is saying is that Winston and Julia's relationship is a thing out of the past. It is like a dinosaur or something else that is extinct. You cannot have relationships like that anymore in the time of the novel. So the room in which they conduct much of their relationship is like some place where something that is extinct everywhere else can still be found.
Relationships like this are extinct, of course, because the Party believes that they are dangerous. The Party does not want any connections between people because those might lead to rebellion.