The Game won't start

[Romulator]

We cannot provide much support for your Intel Graphics Card as Amnesia does not fully support them. Your hpl.log says that the installed OpenGL version is 2.1.0, which is the bare minimum for running Amnesia. Try running Amnesia with the lowest possible settings available in the Launcher.

Unless you can update your drivers for your Intel Processor, there is not much else you can do.

4) I have an Intel graphics card. Can I get support?

All Intel graphics cards are not officially supported by Frictional Games and thus problems can arise while playing the game with them. Only Intel HD cards should be able to run the game. To avoid issues, make sure you have the latest Intel drivers installed and lower the settings. Other than that, no more support can be given in case of further problems.

Your second computer, your AMD, should be more than capable of running Amnesia.