How can I enable Brother printer's two-side printing functionality?
On the page you linked, on the Printer driver download section, it specifically states:


  *Not all features are available for all products.


This is one of those features

Also on the Supported OS page, it likewise states:


  Please note that the available features may vary depending on the operating system.


It appears a Brother is using a generic(ish) CUPS PPD file meaning it’s a one-size-fits-all driver and two sided printing is simply not available. 

It’s not a “popular” piece of advice, but your best bet is to get something with a bit more robustness in driver support like HP, Xerox, or Lexmark.  Brother has been really strong in the Windows space, not so much with Mac.