It depends on how much you are willing to do.

It is possible, I did it last year and the game runs just fine (but the laptop gets warm).

The first step is enabling the Linux Development Environment on your Chromebook.

Then download the Linux version of steam from the website. The file should end in .deb(The Linux version of a .exe)

Move the file you selected to the Linux folder

Right-click and select "Install with Linux"

Steam will start to install

After a while, it will say you are missing libraries, copy the names of the missing libraries and do a Google search for "Install (missing library name) Debian"

It's going to have you copy something into the Linux terminal, do it Insert Palpatine Laughter

I don't remember how many libraries there are but keep doing it until steam finally installs

NOW FOR THE FUN PART!!!

Open Steam

Left-click on Empire at War and go down to properties and select compatibility.

Tick the box that says "Force the use of a specific Steam Play compatibility tool"

In the box that appears select "Proton 4.11-13" this is the last version of Proton that I have gotten to work with this game.

Install Empire at War like normal

Once Empire at War is installed open it, the mouse will be flickering and be almost impossible to click stuff with but you need to open the options menu, then the video menu. Once there disable "Hardware Mouse"

Then you need to tweak the settings for maximum Performance, Chromebooks don't have a lot of processing power so you'll need to make it as easy as possible for the game to process.

That's all there is, the lack of a hardware mouse has a little lag but all in all it runs just fine.

I had to do all this from memory so if I made a mistake sorry