Both are possible but the main problem is that shopping malls don't "go extinct". Flora and fauna (and humans) do.
I don't see any problems with the usage. For years, the media (at least in the US) has been talking about the '
death of the shopping malls', how malls are 'dying out', and even '
dead malls'. The term 'extinct' does see
some usage within the topic.
Back to the original question about differences:
1. Do you ever think that malls are gonna go extinct?-
I would prefer 'Do you think that malls are ever going to go extinct?', but I'm not surprised to hear the word order in your version.
2. Have you ever thought that malls are gonna go extinct?
#1 is asking your opinion about whether malls will ever disappear or not.
#2 is asking if you have ever had the thought that malls will go extinct.
Subtle differences, but they're essentially asking the same general question about your opinion on the future of malls.