For optimum performance and compatibility the display must be connected to the discrete graphic card. I would suggest looking into solving the audio problem associated with the display being plugged into the discrete graphic card. Reason is explained in detail below, if it is too wordy feel free to skip it to the advice about solving the audio problem.
Some more modern games that use cutting edge APIs like Vulkan or D3D12 might be able to cope with cross graphic accelerator output at a cost. However most games, especially older ones, will not.
Fundamentally a display is driven by a framebuffer which holds the image which gets displayed and is controlled by a graphic accelerator. After a graphic accelerator finishes drawing a new image, it eventually gets placed in (or becomes) the framebuffer for the display. However this process only happens easily and efficiently if the graphic accelerator owns the framebuffer of the display.
If the graphic accelerator does not own the framebuffer of the display, such as a game to running on a discrete GPU trying to output to a display plugged into the motherboard, things get a lot more complicated. In the old days such configuration was not workable, be it the lack of support to operate multiple graphic accelerators together efficiently or the fact that doing so is excessively complicated and will always result in poor performance. With modern APIs like Vulkan, which were designed around multiple graphic accelerator cooperation, one can get this to work however one still needs to write the software such that a swap chain is formed to move the resulting images to the correct framebuffer for display.
Now obviously laptops somehow manage to do this all fine seeing how laptops with both discrete and integrated graphics are pretty common now. They have been designed at both hardware and software level to do this which is why it works well most of the time. Desktops are not designed to do this.
Advice for solving the audio problem.
- Make sure that the correct playback device is selected as the default playback device. Especially if your display is HDMI it might appear as another playback device to the OS and take priority over your separate speaker system. To do this one can either use Sound Settings or use Sound from Control Panel. One can generate test sounds to confirm which playback device maps to a physical speaker. Some software, like most games, can only use 1 playback device for audio playback at any given time.
- Try updating the audio drivers for your sound chipset. It could be as simple as a bug which was fixed.
- In worst case try disabling graphic card audio support. If this cannot be done at a driver, playback device or device manager level then one might be able to do it by reinstalling the drivers. For example during installation of the NVidia graphic drivers one can choose an advanced installation which lets one deselect the graphic card audio drivers. I am unsure if AMD has such an option.