In Dorico Preferences / Play / Audio Device, “Suspend audio device in background” is NOT ticked.
My ASIO4ALL is V2.11 beta 2. (V2.11 has now been released, but if beta 2 ain’t broke for me, why upgrade it?)
The ASIO settings are
Buffer size = 1024 samples,
Latency compensation In: 0, Out: 0
Buffer Offset 4ms
None of “Allow Pull Mode (WaveRT)”, “Always Resample 44.1<->48” and “Force WDM driver to 16 Bit” are ticked.
(Not that I know what most of those options do anyway, without reading the manual!)
I just confirmed it works - I can simultaneously play a Dorico score and the audio from a YouTube video, while typing this.
Browser is Internet Explorer 11.
Sorry, but I don’t know what else to tell you beyond that.