Can the RIAA sue anyone outside the US, like in the Middle East or something, for copyright infringement?

Answer 1

Yes. litigation knows no borders.
The lawsuit would have to be launched in the country that the infringement took place.

Answer 2

Any country that is a member of the WTO, which includes China, must legally recognized the rights observed in the author's home country, even if it has no comparable rights for its own citizens. The WTO can impose sanctions or other legal measures against a country that allows infringement to occur. This is the reason virtually ALL CDs are now "produced" in the USA even if they are manufactured elsewhere, as we are the only country that offers a 120 year protection term for mechanically reproduced music.

Many 3rd world countries are not members of the WTO and in some cases they do not observe international conventions of copyright. However, they can not ship contriband outside their boundary, so they do not represent a financial risk to RIAA. It is the developed countries where the money for music recordings is made or lost.