Why isn't Bayek's ring finger removed for the hidden blade?

Without exposing any spoilers, your concerns are explained during cutscenes in the game. Namely, during the Aya and End of the Snake main quests.

If you don't mind spoilers, here is a full explanation:

When Bayek obtains the hidden blade at the end of the Aya main quest he has all of his fingers. There is a cutscene whereby Bayek is testing out the blade. Aya opens Bayek's hand to prevent self-injury when using the blade. Bayek loses his finger during End of the Snake. It is the main quest after Aya. You will see a cutscene when assassinating Eudoros whereby the hidden blade cuts Bayek's finger off.

This YouTube clip shows the End of the Snake mission. Skip to the third minute to see the key cutscene.