TL;DR

Alastor engineered the rise of Vox so he could get someone nearly as strong as himself as a sparring partner, both in media and combat.

Why I think this:

I started thinking about Alastor's relationship with Vox while reflecting on the flashback where he tore Vox apart for wanting to team up. It would be remarkably out of character for modern Alastor to behave that way. When dissing people, Alastor favors being overly curt rather than boisterous. Further, given his deal with Rosie and how he bails Mimzy out, he's more than familiar with the idea of teaming up - both with equals and inferiors.

Based on this, especially in the context of his modern manipulation of the Vees, I think it safe to say his laughter was a calculated response to piss Vox off.

So, why would he piss off someone that he's worked well with? Especially long and closely enough to be on a first name basis with?

Alastor's treats it like a game!

Since we often see their relationship from Vox's perspective, it's easy to see them as rivals. But really, are they?

1. In Stayed Gone, Alastor only acknowledges Vox because Vox explicitly called him out. And yes, he ends with "Oh this will be fun"

2. After It Starts with Sorry, Alastor isn't upset in the slightest at the attempt at infiltration. He has a laugh about it

3. Alastor has absolutely no reaction to Velvette joining the Overlord meeting. In fact, he's smiling through the exchange.

4. After Vox starts slandering the hotel, he continues to pay them little mind, until his plan to break them up

5. Both S1 and 2, Husker keeps asking why Alastor hasn't finished them off yet

So. Why?

My theory is that Alastor arrived in Hell. Thanks to Rosie, he was top shit among Sinners in Pride, and only destined for upward mobility. He continues to mop up Overlord to build street cred.

But then... he's bored. Alexander has no more worlds to conquer. There's no thrill to murder when it's too easy and socially acceptable

So he waits until a suitable rival appears, and Vox fits the bill. His real-life cult shows the ability to run territory and make deals. His technology theme makes him a suitable "rival" to the Radio Demon. As Alastor says, he thought that Vox was "nearly" as strong as he is - and Vox is heavily motivated to keep growing.

And so Alastor steps in and offers guidance. He helps Vox learn the ropes of Hell and build up both power and confidence. Then, at a critical moment pull the rug from under Vox as cruelly as he may in order to ensure Vox takes it as personally as possible.