Is InfoPath Forms Service what you have installed or do you have a full on client version of it on your server?
If its the later I am not 100% sure as I am not a networking guru and I am not overly familiar with using client programs from a server local, but I imagine as long as your users are licensed to use InfoPath it should work. So my initial question for you would be to make sure all potential users of the form have the proper licensing or permissions on your server.
However if it the former you are correct the form would need to be web enabled.
Hope this helps.