“Dorico” is made by a reasonably small team of dedicated professionals, myself included (I write the manual). You’ll often find some of us here – and this week, you’ll find me here quite a bit 
The full Operation Manual talks about MIDI keyboard entry, but the First Steps guide doesn’t: it needed to be a single set of clear steps for people to follow, and not all users have a MIDI keyboard. I wouldn’t recommend that anybody considers First Steps to be a full instruction manual! It’s a beginner’s guide, to get you started. There’s way more to Dorico than could be covered in First Steps (and nor should it, as a number of people have already told me they think First Steps is too big already).
I’ve made a note to add to the full manual that when the caret is extended to multiple staves, playing chords on a MIDI keyboard results in those notes being auto-exploded across the caret’s staves. Not sure why that wasn’t already there, but I’ll get that added in the near future.
One final tip: you don’t need to press the Chords button to start/stop chord input. There’s a key command for that, like there is for many things in Dorico – and that’s Q (for qwords)