Was it copyrighted solely in that country?

Did any of the resulting nations inherit its claims?

At least one game created in the Soviet Union has been the cause of dozens of cease-and-desist orders, lawsuits, and indie games being shut down.

In other words: Yes, or at least most likely.

Technically, if an entity (a state or a company) ceases to exist, it has no more rights, but in almost every case there is a heir at law to the entity. Which means no more and no less that someone else takes over the same rights. Or, the same person(s) that held the laws previously keep them under somewhat different (or identical) conditions or a similar (or identical) name, i.e. a "Soviet" claim might simply become a "Russian Federation" claim.

Also, trademarks may be acquired in other locations independently.

Same situation. Of course the "copyright" for a gun would be rather for building a replica of that gun, not for having it in a game. However, copyright is not the only right you can have on a good. For example, the name or model number (such as AK-47) may be trademarked, or the weapon's design.

For example, Peugeot owns the design pattern "three numbers with a zero in the middle" for automobiles. When Porsche did the 901, they had to change the name to 911 for that reason. Apple apparently owns the design pattern for "black smartphone", or so it seems (that's exaggerated, but you get the idea).

The mere fact that the Soviet Union does not exist any more does not mean that nobody (Izhmash, for example) owns the trademark on the name and/or an utility patent

Quite possibly nobody will care, but you don't know. Quite possibly they do care. You only know when you get a nasty letter from their lawyer, and then it gets very expensive. This is a huge risk.

For that reason it's usually a good idea not to copy something without written permission. You could still have for example a "generic machine gun with a bent magazine" that looks somewhat similar.

With regard the Soviet Union (and it's constituents)

Wiki -International copyright relations of Russia

Quote:

When the Soviet Union was dissolved, Russia as the largest successor state adopted all international obligations of the former USSR, including its membership to the UCC.[38] Consequently, Russia was henceforth considered a member of the UCC (in the 1952 Geneva text) since the date of the adherence of the USSR to that treaty, i.e., since May 27, 1973.[15] The membership of the USSR in the Brussels Convention was equally continued by the Russian Federation as from December 25, 1991.[33]

On June 25, 1993, Russia and Armenia signed a treaty on the mutual protection of copyrights.[39][40] To clarify the copyright situation amongst the states that had made up the former Soviet Union, the Commonwealth of Independent States (CIS) nations agreed on a cooperation agreement in the field of copyrights on September 24, 1993. This "Moscow agreement" declared that all signatory countries considered themselves bound by the UCC as of the date the USSR had joined and would confirm this state with the UNESCO, which administered the UCC.[41] The treaty also defined that the treaty states would apply the UCC amongst themselves, also for works published before May 27, 1973 if those works had been copyrighted before this date according to the national laws of the successor states. This provision was subject to the rule of the shorter term. The intent of the Moscow agreement was to avoid that older Soviet works became copyrighted in only some of the successor states, but would become part of the public domain in some of the others.[42] The 1993 Moscow agreement entered in force in Russia on May 6, 1995.