Many Countries are a member of some Regional Trading Organization, which facilitates trade within a particular continent, or have bilateral trade deals with other Countries. Are there any examples of Countries where at least half of the GDP is a result of trading purely on WTO rules?
The question as posed is probably none.
Small highly trade dependent nations, such as oil rich Brunei, or Kuwait will be trading oil, and oil will provide a large amount of GDP. However WTO doesn't have much to do with the energy trade, there are other agreements that cover oil trade.
Dijbouti has few resources and much of their business is in invisibles (financial services etc) This makes up a large proportion of the GDP (on WTO terms) but this is not a "medium to large country".
The larger countries all have economies that are majority-domestic, Even highly integrated countries like the Netherlands still have more domestic production than production for export.
If, however, the question is "countries that do more than half of their trade on WTO terms", then look no further than China (PRC). Most of China's trade is with the USA, the EU, Japan, Korea, Australia. And these countries are not part of the ASEAN China Free Trade Area. In particular, the US and EU trade on WTO terms (with tariffs, etc...).