Honestly, it seems like a mostly self-selected tag used to indicate culture -- e.g., expectations of working conditions (hours, for instance) that in "normal" business we have long ago realized are actually counter-productive.
Which, frankly, at this point might very well include every company founded since Facebook and including FB. Maybe every tech company post-dot com bubble is spiritually a startup.
This is _precisely_ how I've seen it (mis)used; a (IMO very creepy) need to hang on to those wonder-years that got you there. It's also when you typically see the "visionary" type leaders start heading out and doing it over again.
AFAICT they think it means using kanban boards and having standup meetings.
Another thought leader, Steve Blank, writes that "a startup is an organization formed to search for a repeatable and scalable business model" (https://steveblank.com/2010/01/25/whats-a-startup-first-prin...).
A lot of the "startup type" characteristics of a company can possibly be correlated with one of the above categories. If you don't fall in either category, it would be weird to display those characteristics.
In one case they were bought, so now they were part of a 75k+ employee behemoth. But still, with only some irony, called themselves "scrappy".
In another they're still privately owned, but are over 7 years old, with close to 500 employees, and allegedly #1 in their space. I feel they like to hide behind this "startup" idea because it relieves them of putting on the big-boy pants and accepting that the expense of moving fast being the #1 priority is actually something they're having a hard time paying.