I start a showdown at a battlefield with 1 unit against my opponent's 1 unit. They ride the wind to the other battlefield for their action. Can I still play a challenge as an action before the showdown is resolved at the first battlefield even if their unit is no longer at that battlefield?

Yes, you can still play Challenge as an action during that showdown, even if your opponent used Ride the Wind to move their unit away.

According to RiftJudge FAQ #1265:

"During a showdown you can play action cards and target units on either battlefield. There are no restrictions about where you target during a showdown."

Timing and Chain Sequence

1. Showdown State: You initiated a showdown at Battlefield A. The state is now Open (assuming the initial chain has resolved), allowing you to play [Action] cards.
2. Opponent Action: Your opponent played [Action] Ride the Wind to move their unit to Battlefield B. This creates a chain, making the state Closed.
3. Your Action: Once that chain resolves and the state returns to Open, you have Focus (or it passes to you). You can play your [Action] Challenge.
4. Targeting: Because it is currently a showdown, you are not restricted to targeting units only at the battlefield where the showdown was triggered. You may target your friendly unit at Battlefield A and the opponent's unit now located at Battlefield B (provided they are otherwise legal targets for Challenge).

Note: Once the showdown at Battlefield A concludes, the staged showdown at Battlefield B (created when the opponent moved there) will then proceed, per RiftJudge FAQ #2099.