yes they do. susbcription-based models are doing quite well. besides the big heavyweights, in UK alone there are several smaller and successful subscription-based magazines: the TLS, the economist, the spectator etc. in us sports there's 'the athletic' and its clones.
Maybe I am misreading, but did you mean to imply that The Economist is a 'small' newspaper? It has been around since the 1840s.
Of course they've built it all using AWS and I would love to learn more about how they leverage that platform.
Even with that, NYT has to be much bigger and their profit is only around 2x Economists. Economist is pretty big in most metrics.
However, in this case you're right. They have 1.6 million subscribers, 50% are digital.
Interestingly, a 50% digital rate probably puts them far above all of the other "Old" periodicals.
None of which have actually taken off their runway as far as I know.