Well, I know that the bookstores were full of "Let's learn Hangul!" books aimed at women. I'm sure there are plenty of women who picked up enough Hangul to read the name.
My wife had her own little Korean boom about 16 years ago. She studied for half a year or so and to this day can't pass up reading any Hangul she sees in the supermarket or in magazines.
So, Hangul on the poster is eye-catching to the target audience.

So you're saying I'm underestimating the number of people who can read Hangul (and, secondarily, would make movie-viewing decisions based on its presence)? Definitely possible, since I know nothing about the statistics there.

(From a different "Mitch")

I'm not 100% sure on the rules for putting hangul into katakana. However, I suspect the reason the name was listed was to eliminate ambiguity. I think there is ambiguity in both the グン and the ソク. Because Korean has more vowels than Japanese, this could potentially be either 군 (kun) or 근 (keun - the closest sound in Japanese still unfortunately being グン).

There is a similar problem for ソク. The Korean or Korean-Japanese who knows Japanese knows that Japanese can't end words with as wide a range of consonants as Korean and they know their names don't usually have more than three syllables so they will likely not see ク as a problem, and will assume it is ㄱ. But ソ could be either 서 (seo, which it is in this case, the romanization of the actor's name notwithstanding) or 소 (so). Altogether, that means the reader cannot be certain (unless one sound is extremely uncommon as a character in names) that the Katakana is meant to represent 석 or 속.

That's also a good explanation. I assumed that this kind of ambiguity would be negligible in the case of famous movie stars, which is a fairly limited set, but maybe I'm overlooking some other hard-working actor with a similar name that comes out the same in katakana. (It could also work as a subexplanation of WHY Jang wanted the Hangul there too, if that were the case.)

I could definitely do with more disambiguation like this on promotional materials and DVD boxes for Japanese releases of Chinese movies.

Just out of curiosity, is it common in Korea to include supplementary Chinese characters when writing the names of stars from elsewhere in East Asia, in situations like this?

It seems like another option would be to use Jang Keunsuk's Chinese characters -- wouldn't that remove any ambiguity? Of course, they'd be pronounced in Japanese in an even more mangled way than the Katakana version, and it would hide his Koreanity.

Or is only the family name Hanja-based? I know next to nothing about Korean. The common Korean name Kim is 金 though, isn't it?

about including the Chinese characters, I'm not really sure but whatever mental images of movie posters I come up with my head lacks them - for whatever that is worth.

As for Chinese characters for Korean names, I think most of them have it not just for the family name but for the whole. However, I think there are examples, especially in earlier times when the characters were added much later in the life of the person. I remember a scene in the movie "the president's barber" where the main character had to get characters for his name.