If I play Bewitching Spirit and discard from my opponent's hand Moonlight Affliction, can the opponent still play it as a reaction?

No, your opponent cannot play Moonlight Affliction as a reaction in response to being forced to discard it.

Here is the breakdown of why this is the case:

1. The Triggered Ability: When you play Bewitching Spirit, it enters the board (this does not use the chain). Its "When you play me" ability then triggers and is placed on the chain.
2. The Response Window: Per the provided RiftJudge FAQ #9894, this creates a window where players can play Reaction spells or abilities in response to that triggered ability.
3. The Discard: As the Bewitching Spirit ability resolves, your opponent is instructed to discard a card from their hand. Discarding is a limited action (Rule 422.2) that moves a card from hand to the trash.
4. Reaction Timing: A card in the hand is not "played" simply because it is being discarded. Because the opponent is not playing Moonlight Affliction (and it does not have an ability that triggers specifically when it is discarded), they cannot use its Reaction keyword to cast it. The card simply moves from the hand to the trash.

In summary, the opponent does not get an opportunity to play a card just because it was selected to be discarded. Once it is discarded, it is in the trash and can no longer be played.