How to substitute beetroot for other ingredients into a cake recipe?
There isn't a substitution formula, since beets add moisture, structure, and flavor to the batter.  Any substitution would therefore be complex and highly recipe-specific.

Instead, I suggest that you start with the BBC recipe and make use of the techniques in Stella Park's recipe, such as the brown butter, the foamed eggs, and the double chocolate, all of which could be added to the BBC recipe.

FWIW, beets are an excellent addition to baked chocolate desserts, making them moister, richer and darker.