On Linux the game requires Mono. If you can find an ARM port of Mono it is possible that you could get the game to run by following the directions on our site, although considering the game uses GL and not GL-ES and runs at no less than 1024x768 I'm skeptical that it will work.

Install on Ubuntu
Wait for the package to finish downloading.
Extract the SpaceChem-XXXX.tar.gz archive.
In the extracted folder, open the correct Debian package for your platform by double-clicking on it. Don't worry, Ubuntu won't let you install the wrong one!
If you are on an i386 (32 bit) platform, select the “SpaceChem-i386.deb” package.
If you are on an amd64 (64 bit) platform, double-click the “make-amd64-package.sh” script. When it completes, select the “SpaceChem-amd64.deb” package.
Click the “install” button in the package installation program.

Install on Other Linux Distributions
If you cannot install the Debian package successfully, you can manually extract and run SpaceChem. First, you need the following libraries installed:
SDL
SDL_mixer
SDL_image
Mono 2.0
Mono WCF 3.0 library (Debian package "libmono-wcf3.0-cil")
Mono WinForms library (Debian package "libmono-winforms2.0-cil")
xclip
Next, from bash or a similar command-line interface:
Copy SpaceChem.deb or SpaceChemDemo.deb into a temporary directory.
Extract the game files from the Debian package.
~$ mkdir temp
~$ cd temp
~/temp$ cp ~/Downloads/SpaceChem.deb .
~/temp$ ar x SpaceChem.deb
~/temp$ tar xf data.tar.gz
~/temp$ mv opt/zachtronicsindustries/spacechem/ .
Now you can delete everything in the temporary directory but the spacechem folder, which contains the game.
To launch SpaceChem, change directories to inside spacechem and launch it through Mono:
~/temp$ cd spacechem
~/temp/spacechem$ mono SpaceChem.exe
You can move the SpaceChem folder anywhere you want, but it must be launched from within the spacechem directory.