On of the (numerous) problems with the Borda method is that it requires every voter to submit a complete ranking of all of the candidates. Otherwise, adding up the scores is unfair to candidates mentioned by fewer voters. In your case, let’s relax that standard and insist that each voter rank the same number of candidates. How many voters in your poll used all 20 of their rankings?

There’s a similar issue with your approval voting tally. There’s no reason to think that any given voter approves of her 20th choice, only that she has enough knowledge of at least 20 games to form opinions about them. I have, however, seen this problem (trying to infer approval results from a non-approval ballot) in other places — including at least one academic textbook on voting methods.