Danny Sullivan from Google confirmed that speakable markup now can work for content outside of Google News. Danny said on Twitter "Speakable is no longer restricted to news content; we'll be updating our documentation on this."
Danny added "However, using Speakable markup on any site isn't a guarantee that the Google Assistant will always use it. Speakable also remains a beta feature." You can see the documentation page over here. FYI, I have a feeling speakable markup will go away in the next year or so but I can be wrong. That doesn't mean I didn't implement it here, I did implement it. But I don't think this feature will last - I can be wrong.
This comes from Google saying news content does not only need to come from sites that have applied to Google News for inclusion.
Bill Slawski asked Danny if that includes speakable markup and Danny said yes:
Speakable is no longer restricted to news content; we'll be updating our documentation on this. However, using Speakable markup on any site isn't a guarantee that the Google Assistant will always use it. Speakable also remains a beta feature.
— Danny Sullivan (@dannysullivan) December 12, 2019
So go ahead, implement that speakable markup on your site. Of course, Google will only show it for newsy topics but you don't need to be in Google News as a publisher for it to work.
Forum discussion at Twitter.
