BG1 is the incumbent Bitcoin blockchain while BG2 is Bitcoin Gold. A little research would have helped. You can view the following link for more information
https://www.bitfinex.com/posts/230I believe that should explain further.
I visited the page you mention and it didn't really illuminate the matter.
What does it mean that I can destroy my tokens? Why would I want to do that?
If Bitcoin is split into legacy chain i.e. BG1 and Bitcoin Gold i.e. BG2 why is the sum of BG1 + BG2 approx. 800$ short of price of BTC?