What are the procedures for the countries not included in the 51 qualifying countries?

Dear, if you transit for less than 24 hours, you can use the 24 hour direct transit.
If it’s more than 24 hours, you should apply for transit G type or tourist L type. First, prepare relevant required documents containing your passport and its photocopy, a recent bareheaded color photo, the filled-out application form and other documents.
For L type: round trip air tickets and hotel reservation
For G type: confirmed flight tickets
In fact, if you just transit, transit G type is enough.

Is that still relevant for Israeli passport holders in Kunming airport?

Yes. Israelis are still restricted to 24-hour transit but are also eligible for a 10-year tourist visa.