Créneau can be used, especially in a négative sentence:

Il n’y a pas de créneau disponible.

However, it is more used to mean a time slot in this context, i.e. fixed periods of time like when making an appointment to a doctor which is unlikely the case with your game.

You might then just use place here :

Le serveur permet à cinq joueurs de se connecter simultanément. Il reste deux places disponibles.

Some purists will scream, but many French native speakers in the gaming community will simply use the English term “slot”.

An example here.

The anglicism “slot” is common in French in other technical fields, for instance, in the aviation industry, when talking about the slots assigned to planes for taking off from an airport.

I’d recommend place or emplacement.

As you said fente and rainure don’t fit in this context.

Créneau is closer but is really associated with time slots and I wouldn’t use it.

Place literally means spot, but is also very associated with a one-person “seat”. For example “une place de cinéma” is both a movie ticket and the seat where one person can sit. “There are 2 seats left in the car” is “Il reste 2 places dans la voiture“.

Emplacement is good too. It’s more often used for things that people, but is closer to the definition, and very common in video games : a weapon with “3 gem slots” will have “3 emplacements de gemmes” in French. And since it’s a server and the spots are virtual it wouldn’t bother me to use that word.

I think place is the right way to go, I don’t see how emplacement would fit in this context.

Place would be used in the context of a bus, train, plane or in a car park: In front of a car park there might be a sign “X places libres“.

Showing a list of servers, you could go for:
Serveur AZ123 (4 place(s) libre(s))

But it is also common to use joueurs (players) in your context:
Serveur AZ123 (1/5 joueur(s))