I'd say a general purpose computer at the very least is one that doesn't make too many assumptions about what you should and shouldn't do with it. These ultralight notebooks seem indended primarily for consuming media and the web - which is fine, if that's what you want. But having more ports and more local storage is still less opinionated.
My mom needs a webcam and Skype to chat with her grandkids.
She needs a USB slot so she can load a document from a conference.
She needs flash to play that silly train game she found online that the grandkids admire her for. She needs a decent CPU and RAM because webbrowsing requirements are legit ridiculous these days.
My computers need to be light. I don't need a powerful CPU and, since I run small VMs, not a lot of memory. With containers, the needs are even more spartan. What I do need is a good battery, screen and keyboard.
Were I running simulations over large datasets, I would prioritize a large amounts of memory, fast CPUs and the fastest GPUs I could lay my hands on. And a fast network so I could move the datasets easily. My general purpose computer would have Xeons (E7s and Phis), Nvidia GPUs and Infiniband interconnects across multiple chassis.
My mom needs a keyboard, a mouse and a screen. And a browser. And that's about it.