I'm not sure about the Korean explanation, but it definitely predates the strategy game Starcraft, which was first released in 1998, and was at least five years earlier in beat-'em-up games such as Street Fighter II.
Searching Usenet, I found cheese strategy used on Aug 22, 1993 in alt.games.sf2 in a post called "SF2:HF(Turbo) Ken Strategy Guide".
<=-Zangief-=> He cheats a lot. You will get tough breaks every once in a
while in this fight, so bear (heh) with it. The cheese strategy is just to
use straight up and down Roundhouse kicks, or if you are in the corner, jump
back and use Roundhouse, then sweep/FB or DP when you land.
Here's the cheese strategy involves making simple, easy moves to defeat your opponent. These moves were often described as cheese moves or just cheese.
Another Street Fighter II thread of Dec 6, 1992 in rec.games.video.arcade titled "Cheese glorious Cheese!" includes cheese used a verb and a noun:
But Blanka is pretty much helpless if it is a really
good player who has decided to play this way. Cheese the livin' hell
out of them. And they're more than welcome to try to cheese back,
reason being that the above guy is right about the Blanka-Bison cheese.
A definition was given in alt.games.sf2 on Jun 18, 1992 in "Bison's Cheesepeedo":
"Cheese" is a term used to refer to anything cheap, unfair, or something
that is easy to do, does much damage, and requires no skill. For example,
some people consider the Ken fireball, fireball, dragon punch combo
to be cheese because it can be next to impossible to get out of it (by the
way, I do'nt think this combo is cheese). Of course, the magic throw and
freeze/handcuffs that two-bit Guile assholes use is BEYOND cheese.
The reason people called the torpedo the "Cheesepedo" (I myself call
it the pieceofsh*tpedo) is because it's a dead easy move to execute
(takes no skill at all...just yank back on stick and then forward,
hitting punch button) and does incredible damage, even when blocked.
A no-talent piece of trash playing Champion Edition could (and many
do) know nothing about the game and still beat you with the cheesepedo
by simply mowing across the screen, back and forth.
Capcom had no brain when they put this stupid, f**king move inthe
game. M.Bison "experts" are a bunch of asswipes with no talent.
Nuff said.
Cheese move dates back to at least Apr 6, 1992 in "SF2 TCE Match Ups" in rec.games.video.arcade:
Bison
jumping roundhouse, jab, fierce flame torpedo
neckkick, jab, sonic boom with roundhouse
VERY CHEESE MOVE: strong flame and throw
The very earliest mention I found of this cheese in any form (although I expect there will be earlier ones) was in "SFII (SFI)", posted to rec.games.video.arcade on Jan 27, 1992:
You couldn't choose your character; if you played
on the left, you were Ryu, and if you played on the right, you were Ken. Their
abilities were exactly matched, but not as extensive as in SFII... The two-player version was extremely fierce, though, because the game had absolutely no
cheese.
Finally, a July 1994 rec.games.video.arcade thread debates "To cheese or not to cheese" and an October 1993 alt.games.sf2 thread discusses the (regional) differences between ticking, cheesing, cheating and cheaping. Perhaps cheese comes from a combination of "cheap" (as in a cheap move), "cheat" and "easy".
Wikipedia confirms that yes, it does mean what you think - but the etymology is less certain:
The third meaning is mostly limited to
the United Kingdom, Ireland and
Australasia. It describes a situation
that went awry, perhaps horribly
wrong. A failed bank robbery, for
example, could be said to have "gone
pear-shaped". Less well known in the
US it generated some media interest
when British politician Margaret
Thatcher used the phrase in front of the world's press
at one of her first meetings with U.S.
President Ronald Reagan, with many
reporters being unsure of the meaning
of the term. The origin for this use
of the term is in dispute. The OED
cites its origin as within the Royal
Air Force; as of 2003 the earliest
citation there is a quote in the 1983
book Air War South Atlantic. Others
date it to the RAF in the 1940s, from
pilots attempting to perform aerial
manoeuvres such as loops. These are
difficult to form perfectly, and are
usually noticeably distorted—i.e.,
pear-shaped.
Best Answer
Eighteenth-century occurrences
A Google Books search turns up two examples of "stick in the mud" used metaphorically in the eighteenth century: an item in The Gentleman's Monthly Intelligencer of December 1733 that lists, as one of 14 "Malefactors [who] receiv'd Sentence of Death" at the end of the December 8 sessions at the Old Bailey,
The other occurrence is from just over a year earlier, from The General Evening Post (November 15–17, 1732), reported in William Walsh, A Handy Book of Curious Information (1913):
It is by no means obvious that George Fluster and John Baker owe their alias to a stubborn adherence to a life of crime rather than to being what we would now call "slow on the uptake." The fact that two people caught up in criminal investigations in London in 1732–1733 were known by the alias "Stick in the Mud" suggests that the sobriquet may have enjoyed a brief vogue; but whether that alias came from the criminals' associates or from their government prosecutors is unclear, as is the precise meaning that Londoners in 1733 attached to it. In any event, I suspect that by the 1830s the expression "stick in the mud" was understood to refer to fuddy-duddies and slowpokes, and not to incorrigible outlaws.
Th rest of Walsh's entry for "stick in the mud" is worth repeating as well:
Nineteenth-century occurrences
The earliest nineteenth-century instances of metaphorical use that I could find in a Google Books search of "stick in the mud" and "stuck on the mud" involved the latter phrase. Here are the earliest two. From a review of "The Pleasures of Human Life" by Hilaris Benevolus in The Literary Panorama (1807):
From The Monthly Mirror (July 1808):
In both cases the notion is of being trapped or exceedingly slow-moving (in mind).
The phrase "old stick-in-the-mud" pops up (and flourishes) in the early 1830s. Here are the first three instances that a Google Books search finds.
From William Ellis, "Miru and the Man-Spirit," in Fraser's Magazine (April 1831):
From "The Simpkin Papers" in The Metropolitan (January 1832):
From "Our Birds," in The New-England Magazine [Boston], volume 2 (April 1832):
I couldn't find any instance of "stick in the mud" from the nineteenth century involving a situation connected to criminality.
Interestingly (and consistent with Walsh's note that the expression was popular on both sides of the Atlantic), "old stick-in-the-mud" appears in both London and Boston within a 12-month period. John R. Bartlett claims "stick-in-the-mud" as an Americanism in his Dictionary of Americanisms, fourth edition (1877):
But despite the term's being "very common" in 1877, the first (1846), second (1859), and third (1860) editions of Dictionary of Americanisms don't include an entry for it.
An entry for "stick-in-the-mud" also appears in Thomas Davies, A Supplementary English Glossary (1881):
Conclusion
Although the evolution of "stick in the mud" is by no means certain, I think that the likeliest path of meaning was from a person literally stuck in mud, to a person too slow-witted to take care of himself or herself, to a person unwilling to get out of a rut and try new things, to a killjoy or party pooper. It is possible, of course, that the "mentally slow" and "stuck in a routine" senses of the phrase arose in parallel from the original "person, horse, or coach stuck in mud" sense.