staying beyond the "Entry Before" date

The "Enter before" date has nothing to do with the duration of stay. If your duration of stay is 30 days then you can only stay for 30 days starting from the calendar day after the day you have entered China. You must leave China even if the "enter before" date has not passed, otherwise it would be an overstay of your visa.

Case in point: if the person entered on 15 Jun 2018, then he must depart on or before 15 Jul 2018. If the person entered on 14 Sept 2018 (which is the last day the visa would remain valid) then he must depart on 14 Oct 2018. Thus the example is only a 30-day visa.

Thanks for your swift answer!

This means, if I understand correctly, if you have a 3-month multiple entry visa you could potentially stay up to four (!) time 30 days each
(in the example it is a single entry visa, but assuming it would be multiple entry (M), then it would be possible to stay 15. Jun to 15 Jul, reenter same day and stay to 14 Aug, reenter same day and stay to 13 Sept and still reenter same day and stay until 13 Oct. So altogether 120 days with three intermediate short visits outside China e.g. to Hongkong. Right?

That is largely correct except you can't enter on the "enter before" date but the day before that date. This means you can stay for around 118-119 days. I am not completely positive that Chinese authorities will issue a 3-month multiple entry visa though. Europeans usually can only get single-entry visas (and they still check stamps for visits to Turkey).