It’s a very short article so I just quoted half of it.
Question for the pilots among us: If ATC is telling you to land on Runway 18R, do they say Eighteen R, Eighteen Right, or Eighteen Romeo? And do they just say eighteen or do they say one eight?
To direectly answer the OP’s question as asked …
By ICAO standards it should be “one eight right” or “one eight left”. Nothing else, period, amen. And that’s pretty well exactly what happens every time everywhere in the English speaking part of the world.
In countries where English is not the local native language, it is common that ATC comms between controllers and pilots who both natively speak the local language are in that local language. Which suggests that the comms between this tower and that airplane might well have been in Korean. Not strictly ICAO-kosher, but not so bad as all that. And may well be fully in accordance with local regulations, ICAO be damned. That technique does have some advantage for non-standard situations where just hashing it out in your native language beats hell out of trying to use magic buzzwords and phrasebooks to maybe eke out saying sorta what you really mean in pidgin English to somebody else whose knowledge of English is pretty well limited to the same phrasebook.
How exactly Koreans handle this is beyond my experience. My experience does include a lot of Spanish-speaking Latin America and the Caribbean. As a rule, what I’ve heard follows the ICAO standard phraseology very closely, just said with Spanish vocabulary. E.g. “uno ocho izquierda” or “uno ocho derecho”.
Bigger picture, most wrong runway landings are not a result of ATC mistakes nor comm terminology confusion. The vast bulk are pilots mistakenly identifying this aim point on the ground as the place to land, but being wrong, and they should have been aiming at that nearby aim point instead. Oops.
Sometimes that’s personal left-right confusion / situational dyslexia. IOW “Your other left, stupid!!”
Other times it’s expectation bias where you “always” land on 27L, except for tonight where it’s 27R, and despite having heard and repeated back 27R, you still somehow see, target, and land on 27L just like always. While your partner in the cockpit falls into the same trap for the same general reasons. Oops.
Other times it’s confusion between a raft of runways and parallel taxiways where you’re confronted with 6 strips of pavement separated by 5 strips of grass / dirt, all of which look more or less the same from 8-10 miles away.
As to this airport specifically …
Ref some googling, Gimhae seems to be two parallel runways, with a single taxiway on the outboard side of each and none up the middle. One outboard side of the airfield has airline ramps, cargo, etc., while the other side is military. See PUS - Busan [Gimhae Intl], KR
And seemingly they operate the airport as two separate halves most of the time, but are now using the “military” runway for commercial since commercial traffic has grown beyond one runway’s capacity. What is interesting to me is the subject airplane was supposed to use the “commercial side” runway but instead landed on the “military side” runway. Which sorta suggests confirmation bias was working in reverse. Hmm.
Unless the pilot flying was a reserve military pilot who flies ROKAF heavies in and out of the same airfield and went on “human autopilot” for the approach as if he were flying a military mission.
Doesn’t seem likely, however.
Or, you fly 95% of your ops into runways 36, but today the wind is blowing “backwards” and you end up on 18. So you always land on the e.g. left, but today that same bit of runway is labeled “right”
Here is the ICAO Aerodome Chart for Gimhae.. I’m betting for the pilots among us, that chart is a lifesaver. For me, it’s a lot of information packed into a small space and thus quite confusing. For example, I can easily see 36L, 36R, and 18L, but where is 18R? I’m going to take a guess here and say it’s the other end of 36L but I don’t see the label on the chart. Another question, if there are only two runways, why are they numbered 18 and 36? Why not Runway 1 and Runway 2?
If anyone’s interested, here’s the Instrument Approach Chart.
ETA: Ahah! I finally found 18R on the aerodrome chart. I give my students grief for using different fonts/colors for the same type of information when they make infographics. What’s with hiding the 18R label where it is, a different place in relation to the runway than the other 3 labels, and in a different color to boot?
The numbering refers to the approximate compass heading the runway is aligned with. Runway 36 goes north, runway 9 goes east, runway 18 goes south (and is by definition the opposite end of the same pavement as runway 36) , etc.
When there are more than one runway that are parallel, the naming rules call for labeling them left, right, and if necessary, center.
So 18R and 18L are the right and left parallel runways pointed very nearly due south.
WAG from a non-pilot:
Because 18R doesn’t start where the concrete starts, but starts at the mid-point - which makes it approximately the same usable length as 18L/36R.
@Zakalwe nailed it. That’s why it’s different, but I agree 100% with @Monty that that is sloppy workmanship and/or a sloppy charting standard.
FWIW, lots of different agencies / countries publish charts. Each of which use their own set of symbology. Even US military charts don’t look like US civilian charts: different agency, different symbols, same reality on the ground. The cited ICAO chart for Gimhae resembles the standard the US DoD uses, but is not the same. It looks quite different from a US FAA civilian standard chart.
The vast majority of commercial aviation uses charts by the commercial provider Jeppessen, not the ones published by governments. That way they’re all the same format the world over. It’s a bit of a religious topic, but nearly everyone agrees Jeppessen’s standards are far better than ICAO’s.
IOW it’s a mess. Caused mostly by your usual international stew of good intentions, bureaucratic inertia, a certain amount of local pride / NIH syndrome, and the genuine need for backwards compatibility and reasonable degrees of interoperability.
The Jeppesen version of the airport diagram.
If the crew were using Jeppesen they would probably be referring to the moving map display which is interactive, can be zoomed, panned, and always shows the runway names regardless of zoom level.
That’s one of the approaches to the other runways (36). No doubt due to the terrain north of the airport the only approaches to runways 18 left and right are offset and require a visual “circle to land”. I’ve attached the VOR approach as it depicts the visual segment while the other one, the RNP approach, doesn’t.
This could be one of the factors leading to the misidentification of the runway as instead of being spat out the bottom of the approach perfectly lined up with the correct runway, they would need to manoeuvre visually and there is opportunity there to become focussed on the wrong one or even just forget which one they’re supposed to land on.
Edited to add the green highlight on the inbound track.
I feel like I just won some sort of award. 
Back in the day our coffee was served in distinctive squat but wide airline-branded styrofoam cups. Which were a poor choice for use in a moving machine since they sloshed much more easily than would have a taller more typically-shaped cup of the same capacity.
Anyhow I used to fly with an old Captain who was a bit of a cartoonist. He’d elaborately decorate one of these styros with “Pilot of the Quarter” and all sorts of filigree and braid & such. He really was pretty good.
When you did something extra smart (or extra stupid), he’d make a great ceremony of presenting you with your award: the customized PotQ coffee cup of the trip. Which you were supposed to keep and use for the next couple of days together.
He’s long retired and probably dead, but in memory of that fine guy whose name I don’t recall, I hereby present you with the “Aviation Poster of the Week” award cup. Suitably (virtually) decorated of course. 
I accept this award with all humility and cheers to all (it doesn’t have coffee in it though ).
Thanks for a great story. Sounds like a fun guy to fly with.