It's a pun on the word 'djinn', which is a supernatural creature in Arabian folklore: this where we get the English word 'genie' from. The joke is that this word sounds almost the same as 'gin'. What's interesting is that we use the word 'spirit' for both of these categories of things: genies, fairies and so on are 'spirits', and so are gin and whisky.
'Chicks' is a derogatory word for women, and the dictionary definition of 'dork' is "a contemptible, socially inept person". The suggestion is that 'real men' can handle whisky, while gin and tonic is a 'sissy' alternative just for women and for stupid, uncool, nerdy men.
The narrator says that the djinn/gin wordplay is poor, but it's not as bad as the 'Stiff Drinks' pun. Personally, I think the Djin joke is quite good, and that Stiff Drinks ( in the context) is brilliant. But that's just my view :)