Advancing Tzolk'in past the end of the game
The rule for using this power right before any food day would still apply normally to the final food day of the game.

It is not possible to use this privilege to avoid Food
Days. If the next day on the Tzolk'in gear is a Food Day,
you may still advance 2 days, but the new round will be
the Food Day that was skipped over.

Turn 27 is a food day; it just so happens that it also is the final food day that ends the game. So you can turn the wheel 2 spaces, to 1 space past the final food day space, and then play the final turn like you normally would.
This matches what you say happens on Board Game Arena. I think it does make sense, because it’s not so much that the game is supposed to last 27 days, but rather that the game ends after the 4th food day. All food days normally happen on the indicated space on the wheel, but with the skip a day power and the quoted rule above, it is possible for a food day to take place 1 space later instead.
This can still be useful to do in turn 26, because it means that for the final turn, all workers are one space further along their wheels than they would have been otherwise. This could allow you to take an action that you couldn’t have otherwise, or also mess up your opponents' plans by forcing them to pay extra corn to take the action they were planning on taking.
The only way in which the power is different on turn 26 than at any other time in the game is that normally, the total game length is shortened by 1 turn for each time someone uses it, but that doesn’t happen if used at the end.
This interpretation was discussed and confirmed here: https://boardgamegeek.com/thread/910514/double-wheel-move-penultimate-space