I'm new to Linux and I'm very clueless on what to do to install the game properly on Linux (I'm using a Chromebook). I already unzipped the game and tried to run Pumpkins_Client.x86_64 using the Terminal app but I must but doing something run because it's not running. Can I have help on how to install it?

Assuming you have a compatible processor and etc., then you need to do this via Terminal to make the file executable (but if you tried to run it, it should have said something?):

chmod +x Pumpkins_Client.x86_64

And then to run it:

./Pumpkins_Client.x86_64

What follows is a basic overview of what the requirements even are, but it doesn't look easy for Chromebooks, and I'm afraid you might not have much luck. I can't really test it properly since I don't own a Chromebook, and performance may be bad even if you get it to work. Also partially, based on this thread:

/t/5424951/how-do-i-install-this-on-linux-for-chromebook

In short, Chromebooks are a bit more like Android than Linux, but if you have:

1. Intel or AMD (x86_64) processor, not an ARM processor

When you look at your CPU, it should say AMD or Intel. If it says MediaTek or Qualcomm Snapdragon, you're pretty much out of luck.
And even if you somehow get it to run on an ARM system, it will probably be unplayable. :(
You can check either via:
Diagnostics app: App Launcher -> Diagnostics -> Search for a CPU section
URL: Go to either chrome://system or chrome://diagnostics and I assume it should have cpu or cpuinfo somewhere in the page.
System info app: You can try installing a third party system info viewer, like Cog maybe, but the other options are preferred.

2. Enabled "Crostini" (apparently the "Linux development environment" for ChromeOS)

I assume you have this since you mentioned you were already in the Terminal app, but to enable it, you can go to (based on what I'm reading):
Settings -> Development -> Linux development environment
And enable it, which should install a basic Debian container.

Assuming you clear both of those requirements, would then  move the extracted files into the "Linux files" folder, access via Terminal, do chmod +x on the file to make it executable, and then run it via Terminal using ./Pumpkins_Client.x86_64

There isn't any further installation procedure, but it might be missing some graphical libraries. Anyway, please check first if you have Intel/AMD processor at least, but I wouldn't hold my breath for running this well, sorry.