My understanding of the tax withholding on prizes for non-residents

**************
Disclaimer: I'm not a lawyer or accountant, and this is not legal or accounting advice.

The following are my personal opinions on the matters of Korean taxation of prizes won by non-residents or foreign corporations.
If in any doubt be sure to seek professional counselor's advice.
**************

Book about Korean taxation. (tax withholding on page 333)
https://www.nts.go.kr/eng/data/KOREANTAXATION2012.pdf

All double taxation avoidance agreements with Korea.
http://www.nts.go.kr/eng/resources/resour_02.asp?minfoKey=MINF7620080220173406

1. Countries on the Samsung's list

From what I can see, the countries that Samsung listed in the e-mail are the countries for which:
a) either there is no mentioning of so called "other income" in the tax treaty, like for example in the Korea - USA treaty (in scope of tax treaties other income usually means income that is not mentioned in any of the articles)
b) or there is a specific article about "other income" being taxable only in the country of residence, but through some additional paragraphs in that article, that other income is still taxable in Korea, like for example in Korea - Bangladesh tax treaty article 22

In both of these cases tax on prizes for non-residents must be withheld.

However, if there are some local taxes that you must pay on prizes (check your local income tax law), then you should also find the articles in tax treaty where getting tax credit for tax paid in other country is explained. This is usually called something like "relief from double taxation".
I don't know if Samsung will provide some hardcopy proof of paid taxes in Korea, but even if they don't I think that such proof should be possible to obtain directly from Korean tax authorities.

2. Countries not on the Samsung's list

On the other hand, I've checked several countries which are not on the list that Samsung gave us, and all of them had an article about "other income" (usually article 21 or 22) which in my opinion without doubt says that other income will be taxed only in the country of residence.
There are usually some additional conditions in paragraph 2 of such article, but I think that for most, if not all of us, those conditions are not applicable, so therefore I suppose that prize money should not be taxed in Korea according to such tax treaties.

Since that is (in my opinion) effectively tax exemption, and since in the instructions for the filling of the "application for entitlement..." it's explicitly said that the "application for entitlement..." will not be submitted by non-resident which is exempt from Korean withholding tax according to the relevant tax treaty, then I would say that we from countries that are not on the list should not submit anything and that Samsung hopefully shall not withhold any taxes on our prizes.
However, one can only hope that it will indeed be so.

Anyway, if some tax is nevertheless withheld, and you believe that it should not have been, then there are probably two options:
a) to ask Korean tax authorities to return it (I think that there is some procedure for that and that it can take up to six months)
b) if prizes are considered taxable income in your country then instead of asking the tax return perhaps the tax withheld can be used as tax credit in your country as it is explained in tax treaty under the article about relief of double taxation

Final note:
Be aware that in some countries it can be tricky to determine if prizes are taxable income or not!