I think your specification is already misguided:
that they MUST be on a desktop (or laptop) to properly use the system
Such classifications aren't what you actually care about. What matters are specific properties that make your site work well with the device or work badly/not at all.
If the properties are understandable for the end user, I'd mention them. For example it could be:
- You only support a specific operating system or browser
- The size of the screen needs to be big enough
- You don't support touch devices.
I also recommend giving a short reason for why that's a problem, else the user might simply assume you're incompetent.
From your comments I gather that your website actually works on tablets and mobile devices, but the extensive text input can be annoying on a touch device.
This means that:
You should talk about input methods (keyboard, mouse), not the form factor of the computer.
You should phrase this as a recommendation, not as a requirement.
You should mention that you recommend this because there is a lot of text to type, so the user can make an informed choice to continue if they're fine with entering a lot of text.
Perhaps they have a tablet with an external keyboard where typing is easy, perhaps they're happy to type longer messages on a touch screen or perhaps they don't even own a proper computer at all.
I'd phrase it something like:
We recommend using a physical keyboard instead of a touch device since you will need to enter and edit longer texts.
As an icon you could use a keyboard.