There is no limitation built into the demo that would prevent deploying it on IIS.
The rendered code (ASP.NET WebForms) should have three parts:
1. The empty div with id set to the ID of the control. You will find it at the place where you put the control.
2. References to the JS libraries, loaded from URLs that include "/WebResource.axd?"
3. JavaScript initialization code. You will find it at the bottom of the page. It starts with the assembly identification which looks like this:
<script type='text/javascript'>
/* DayPilotPro: DayPilot, Version=8.1.3460.0, Culture=neutral, PublicKeyToken=426941954f05e7fe */
...
The <script> section should list the settings.
If the Gantt control doesn't appear at all there is probably a JavaScript error that you will see in the browser JS console (Ctrl-Shift-I in Chrome, F12 in IE/Edge).
In Chrome you might see something like:
"Uncaught ReferenceError: DayPilot is not defined(…)"
or
"Uncaught TypeError: DayPilot.Gantt is not a function(…)"
This means that the libraries from part #2 were not loaded properly. Let the page reload with the Developer Tools enabled and check all WebResource.axd links in the Network tab of the Developer Tools.
The response should contain JavaScript code. You might see a server-side error instead, maybe an exception description. The error message should tell you more about the cause - most likely it's some kind of IIS misconfiguration.