Not saying you're wrong, just throwing a wrench into the works because it has been on my mind and I'm curious what the hive mind has to say.
The deadline part is a more onerous constraint but still I like his definition better than yours because of the hobbies that have negative consequences (like the mountaineering).
I think the best definition would be a modification of "A true hobby is something that you don't do for money and that has no deadlines attached." but instead of saying what it isn't (deadlines, money) say what it is:
A true hobby is a personal activity that has sentimental value.
The meaning of 'personal' here is that it would be detrimental for the activity to be attached to the world (through things like deadlines or money) and it has sentimental value i.e. it is not a chore but is actually enjoyable.
Another observation is that you sometimes want to share personal things with others but only if they belong to the group you trust with this particular secret. Hobbies can therefore have attachments but only to the world of that hobby (some niche community probably). This world can then become a gateway to the real world again since if you rise in the ranks of this community you become a part of the leadership that straddles the border between the community and the real world, the members of the community will often pay for this 'protection' - as an example, pro gamers legitimize the hobby of gaming since it becomes a possibility, however unlikely, to make a living playing games. This protection allows hobbyists to fully engage in their activity without concern for reality, hiding behind the delusion of one day becoming pro or in other cases staying relatively anonymous or legitimate due to the more extreme people taking the spotlight. For those who stand the vanguard it is a cutthroat life very much attached to the real world (deadlines, money, training, hard work) the hobby has therefore ceased to be a hobby and has become a job or lifestyle.
I think that's a little too specific and doesn't fit a lot of hobbies. People do often make a little money from their hobbies: fixing up and reselling old cars, thrifting and selling on eBay, refinishing furniture, putting up videos on YouTube.
Also, many hobbies have time-critical components. Even all-American pastimes like sports require you to not miss the game.
I'd crystalize it like so: A hobby is something you sink time into where failure has no negative consequences.
Since people like to pick nits here, that probably needs a couple of qualifiers. The sunk time itself can be considered a negative consequence. And the failure may have negative consequences within the hobby — if you accidentally crush your ship in a bottle, you aren't gonna be happy.
But the negative consequences of failure don't bleed out into anything else in your life. You have no need to succeed. That encapsulation of failure is what I think makes hobbies safe and thus encourage fun and a sense of play.
The reason it's so often disastrous to turn your hobby into a job is exactly because of that reason: it means you are now adding real stakes to the game. If you failed frequently and safely when it was a hobby, that was fine and you might still love the hobby. Once those failures matter, it can upend the whole cost/benefit calculation.