If you want your game to communicate with your own host then you'll need to add the appropriate headers to your web application that is accepting analytics data. You can learn more about this here: https://developer.mozilla.org/en-US/docs/Web/HTTP/CORS

Essentially, your PHP script needs to know how to tell the player's browser that it is okay to send the data to your server. I haven't worked with Unity directly, so I can't give you any specific instructions, but it shouldn't be too hard to figure out how to get it working by searching online. 

Hope that helps!

CORS is a way for a server to say what web requests it is prepared to accept from other sites.  It's difficult to know what itch could do to foul this up, since itch has no control over your server.  However, if you hosted your game on your own server, there would be no need for CORS.  Cross-Origin Resource Sharing only applies when the request is cross-origin, and it is not if the game and the analytics service are hosted in the same place.

There are a couple of traps with CORS.  The first is that for some types of request, CORS has to be explicitly requested by the code running on the browser.  The second is that a CORS request is split into two, with an initial "preflight" request being used to check for the presence of the CORS headers.  This is done with the HTTP OPTIONS method, so you should make sure your server is sending the CORS headers in response to OPTIONS as well as GET/POST.