Your charger appears to be an example of a genuine Apple, as I now have seen others for sale with the same markings, sold as genuine Apple. I don't remember ever noticing that Dongguan Samsung, but apparently is just one of Apple's suppliers.
You COULD try replacing the magsafe board (inside the macbook). iFixit.com has the part, seems to be about $20, and maybe 30 minutes to replace.
If you want to get a new magsafe charger, BestBuy continues to sell Apple-branded 60w for about $80.
After that event (charger not charging after extensive use) one of my external harddisks (Western Digital 3,5" 500GB) suddenly failed which I used with my Mac mini, recovering the files etc, only recently I could return back to the "fake charger" topic.
Well yes my charger indeed looks like genuine. Particularly the printings on the sides looks like the genuine and the weight (174g / 219g w./without MagSafe cable) is
almost like the genuine which is 220g with MagSafe cable.
Though the magsafe board (or connector or socket) is mistreated / battered a bit, I don't think it would cause the kind of problem I had. Once the charger stopped charging the MacBook, it would last a minute or two no matter how carefully I placed the connector to its place. I usually had to unplug the charger from the outlet and rest it for about half a minute then reconnect, only then the charger would start charging the MacBook. Once it didn't even start charging. I had to use the MacBook's battery for an hour two. I don't think a real genuine Apple charger would cause such a problem.
So I've restarted searching on the Internet and found this:
OEM MagSafe Chargers vs Cheap Imposters: Teardown for Truth - beetstech.com blog June 16, 2017
On this blogpost, one particular thing drew my attention. It was saying if the System Report>Hardware>Power>AC Charger Information displays Serial Number as 0x00000000 then it's a fake charger. I've connected my charger and looked up that number. Here you are:
The Serial Number is 0x00000000 (!)
