You can try to define "Personal Computer" this way, but historically the name "Personal Computer" just meant a computer that you use alone, instead of being one user of a computer at the university or the company you're working for. Which then was not your PERSONAL computer. That was the major reason for calling a computer you use as the only user (and that sits on or under YOUR desk) a Personal Computer.
ChromeBooks are mostly Terminals, even if you own them the applications run elsewhere. Surely not dumb terminals, but still terminals, just personal terminals that you can own and carry with you instead of going to where there are.
But people easily forget that once computers were something you had to go to to use them as one user among others. You didn't own them and you could not carry them home (or to your office) and use them just for yourself. Both the "Personal Computer" and the "Home Computer" changed that in this way ChromeBooks are a kind of Personal Computer.
Of course then the IBM Personal Computer (PC) became the standard Personal Computer and then what once was a description became nothing but a name ("PC") for a certain kind of computer (a computer with an Intel CPU running Windows or Linux that is and has to be fully cared for by the sole user). Since then people think a "PC" is exactly that. And they're somewhat right, because meanings of words change over time.
An iPad is a "Personal Computer" (you can carry it home and use it as the sole user), but it certainly is not a "PC". A ChromeBook also is a Personal Computer but maybe not what people came to think of a PC (some people not even call a laptop a "PC", they call only desktop PCs "PC").
It's murky, but quite easy to get to the bottom of. Fighting about "is a ChromeBook a PC?" is pointless though when everyone uses a different definition of what the name or description of a "PC" or a "Personal Computer" is supposed to mean. Most people who fight over words only do that because this is often the first time they even thought about what the word means at all and then they're already invested in having to win an argument they started without even knowing what the word they are fighting about actually means and where it came from.
(And actually a "computer" once was something you used to compute things with. The name "computer" was a descriptive name like "screwdriver". Even earlier "computer" was a job description before robots started to do the job... But just as "PC" it became a name instead over time and is not a description anymore because most people don't use them to compute anything. As a name it immediately loses any sense as soon as you start to wring any meaning from it because it has long stopped to be used in the form of a description for what you do with that thing. So don't fight about names, it's useless. It's like asking someone to mill your wheat just because his name happens to be "Frank Miller". At some point in the past one of his forebears certainly did that, but now it has just become a name attached to him through inheritance and is not a description of what he does anymore. Maybe he's a butcher and then people use the name "Miller" as an argument on