This the correct download page: https://www.wolfram.com/engine/
You get a file `WolframEngine_12.0.0_LINUX.sh` about 1 GiB.
Click the Download button on
https://www.wolfram.com/developer/
Its linked from the article.
I see, thank you. I must have clicked that link to sign up for a developer license, but somehow I don't remember being offered to download the thing.
I feel silly now, but that was pretty confusing.
So I was curious and signed up for a developer license. I got to the confirmation page, which helpfully told me to run "WolframScript" to activate the license. But there was no download link, so I googled around and found this[1] page. They seem to only have packages for Fedora and Debian-based systems, but no biggie. I used `debtap` to convert it to a package that pacman can install, and then, moment of truth...
Uhhh... okay? And where do I get this WolframKernel from? I looked around my Wolfram Account page, and I don't see anywhere I can get this from. Google also doesn't help me here.So... it seems you probably need a full Mathematica/Wolfram license before you can use this anyway?
Well, that's disappointing.
EDIT: OK, you can actually download it from [2]. My bad.
[1] https://account.wolfram.com/products/downloads/wolframscript
[2] https://www.wolfram.com/engine/