Comma used to seperate parts of a sentence or items in lists or to create an absence of sound(as a breath mark)!
If all the items are applicable to the verb, you can seperate them with a comma, without using the same verb again and again.
He wants to play basketball, play volleyball, play tennis .
instead you can write;
He wants to play basketball, volleyball, tennis...
instead of too many play here only comma is enough.
When you are writing series of events like these and ending it with another verb or another type of event you can do this;
He wants to play basketball, volleyball,..., + and / or + go for a walk, sight seeing, skiing....
Each item is seperated with a comma except the items after and/or cause play verb cannot be applied on "a walk". Instead you can seperate items that are applicable to go after seperating them with and/or.
In your context however you are trying to imply that this person would like to do 1 of 3 different things;
He wants to play basketball, or volleyball, or go for a walk.
Comma allowed us not to use play too many times but still you have to use or to imply it is a choise between these options.
When there is a choice between things you can also do this;
He wants to either play basketball, volleyball, or go for a walk.
by getting help from adverb either you can ease your pain and get rid of multiple or usage too.
What else we can do with it?
You can keep using comma without in need of seperating with "and / or"
He wants to play basketball, volleyball,..., go for a walk, sight seeing, skiing....
commas before go here is applicable to the play and commas after go is applicable to it self.
You can use it as a second of breath or a shush mark.
He wants to play, many things. (after play breath taken)
He wants to play, even if it's not safe for him to play. (after the first play breath taken or a momentarily shush takes place)