Depending on who you ask, it's one or more of:

1) So that the "free articles this month" counter doesn't decrement for stories you don't actually read.

2) So that they get metrics on which articles people actually read vs. loading in a tab and forgetting about.

3) Forcing an interaction manipulates your psychology so that you pay more attention to the page, increasing engagement.

I vaguely remember implementing this exact thing for at least two clients, and if remember correctly the reason is that such a 'show full article' button allows anything 'below the fold' (meaning the button) to be more prominently visible.

It's a rather ironic that I had to turn off my uMatrix filters to get the full 'experience' of that button.

Because it's the mobile version of the site. That button doesn't appear on the desktop version.

I’ve noticed a lot of news sites have started doing this. I assume it’s something to do with collecting analytics?