Your resting calories are calculated by your weight and age. For a man it is usually around 2000 kcal per day. 10 hours into the day you should have 'burned' 10/24*2000 just by being alive 10 hours in a day. The watch simply needs to know what time of the day it is to calculate this and therefor you don't need to wear it, as the apple watch actually does tell the time.
People have to see that calorie stuff more relative. It depends on your age, your height, your metabolism, the bacteria in your digestive organs, your eating habits* and other factors. Not every person sitting in a chair and doing nothing all day will need 2000kcal.
Also while we are at eating. There are three different basic bacteria cocktails that people all over the world can have (much like blood types), scientist found out that people that have a higher percentage of these and those bacteria can e.g. digest proteins better, while others with one of the other bacteria cocktails may digest carbohydrates better. - I know that sounds like some weirdo made it all up, but it is really true! (the ones who digest protein better, for example will fart more when they eat stuff that has more carbohydrates or fat and may **** out some of it without utilizing all for their body. - the protein guy is just an example here, could be other way round, too. I don't remember the details of the study right now).
Also, what scientist are just researching is, that they found out that there are different "types" of calories. So that the calculation that people used over all the years, that carbohydrates have 4,5kcal per g and so is not true anymore and is dependant on the food the carbohydrates, proteins and fat are in. This is not well researched at the moment and they only have something like a small hint to it by now.
That is why some people try and try and get nothing but headaches, when they count calories and maybe do a diet and nothing changes. But if you don't get crazy about it and get unhealthily thin or fat the 2000kcal for doing nothing is a good rule of thumb estimation thingy.
But don't forget, even if you think you are doing nothing, you might burn more calories than you know. E.g. a student, that sits on the desk and is thinking for ca. 6h, at say the age of 24, will probably burn 2400kcal a day.
(*if your body is used to not getting fed so often, it will learn to save the calories better and may even use/need less calories, when you do nothing).