My Spectral Centaur and my friend's Master Yi were in a showdown at Forbidding Waste. I ambushed in Kha'Zix while he only had Master Yi there, so his unit was alone. Then he responded by ambushing in his own Kha'Zix. Does my Kha'Zix still get the +2 Might and 2 XP since his unit was alone when my Kha'Zix entered/defended? Or does it not happen because by the time the chain finishes, we both have 2 units there?

Your Kha'Zix, Mutating Horror will still receive the +2 Might and 2 XP.

According to the rules and the way triggered abilities interact with the chain, here is how the sequence plays out:

Chain Sequence

1. Your Ambush: You play your Kha'Zix, Mutating Horror using [Ambush] as a [Reaction].
2. Trigger Condition Check: When your Kha'Zix enters the battlefield, he gains the combat designation (Attacker or Defender). His triggered ability reads: "When I attack or defend, if an enemy unit is alone here...".
3. Ability Added to Chain: At the moment your Kha'Zix enters and gains the designation, the game checks the state of the battlefield. Since your opponent only controls Master Yi at that location, the condition "an enemy unit is alone here" is met. Your ability is added to the chain.
4. Opponent's Ambush: Your opponent responds to your trigger by playing their own Kha'Zix, Mutating Horror using [Ambush]. This goes on the chain above your trigger.
5. Resolution (LIFO - Last In, First Out):
   • Opponent's Kha'Zix: Resolves first. It enters, gains a combat designation, and triggers its own ability.
   • Your Kha'Zix: Resolves next.

Why the bonus remains

The trigger for your Kha'Zix was already placed on the chain at a time when the condition ("enemy unit is alone here") was true. Because the condition was met at the time the ability triggered and was placed on the chain, it does not matter that the battlefield state changes before the ability actually resolves.

As stated in the RiftJudge FAQ #9849: "Because you are playing into a battlefield where the opponent has only one unit, the condition 'an enemy unit is alone here' is met at the moment Kha'Zix enters and gains the [combat] designation."

Therefore, your Kha'Zix's ability will successfully resolve and grant the bonus.