Board Game Arena

The game's rules say that in the case of a tie "both players share the victory."

Since that is not an option on BGA (why isn't it?) how is it determined who is awarded ELO points?

A tie, in ELO terms, is half-win, half-loss. You lose a little ELO if you tie against a lower-ranked player, and win a little ELO if you tie against a higher-ranked player. A tie between same-ranked players is the expected result, so no ELO change would occur.