I would like you to test the following configuration:
Set it as in the screenshot.
Also, please check the graphics options that you have in your game, that would also depend on how the displays would behave.
If you have the option to set multiple displays in the game, getting the image in the external display would be possible.
Another way to go would be, setting a single display, the external, if the main goal is to get the game there. Additionally, you could use clone displays to get this done as well.
Are you using the generic drivers from Intel? or the ones provided by your OEM?
The recommendation while using OEM systems is to download and install the drivers from your computer's manufacturer website.
This is to avoid loosing any special features or settings while using the generic drivers from Intel®.
Generic drivers, please make sure you select the OS currently being used: Drivers & Software
I look forward to your outcome with this.