Threads like this always go the same way.
OP asks a straightforward question, lots of people get offended, people queue up to say BMI is rubbish "because bodybuilders", everybody gets sidetracked by vanity sizing and we end up going round in circles.
There's so much emotion involved in the whole thing, and with different people having different definitions of "fat" nobody is ever going to agree.
There is a national problem with obesity and threads like this illustrate why it's so hard to tackle it. People get so upset around the words "fat" or "overweight" that it's impossible to have a conversation without it descending into hyperbole.
It's always refreshing to be around groups of runners (I presume other sportspeople are the same? I'm quoting runners because I know lots) because they tend to talk very honestly about any weight gain and how it impacts on their performance.
They might say "I've gained 7lb, it's on my tummy, and I need to shift it" without any emotion attached. It's a frank and factual approach.
Whereas in the general population it would be more "I've gained 7lb, I feel fat and it's really getting me down."
In the first example, you can reply to the runner and talk about ways to shift that weight. But in the second example that person is upset, they've told you they feel crap - they want support and reassurance they still look great, not a conversation on healthy eating.
Most people, IME, find it difficult to talk openly and honestly about weight. Which from a public health perspective is disastrous.
To answer your question OP, yes I would probably consider a size 14-16 person at 5ft 8ins to be "fat." But it doesn't matter what I think or what anyone else thinks. All that matters is if you're healthy and if you feel good at the size you are. If not, change it.