1) Espionage through psychic remote viewing, which leads to...
2) Interdimensional travel between two points on Earth by taking shortcuts through the Upside-Down. Which leads to...
3) Trapping demogorgons in cages using cattle prods, for experimentation/weaponization
In the "flashback" scene, the Russians knew that the Americans has somehow opened a portal and were using it to spy on them, so they were trying to use their own machine in Russia to do the same. Can't fall behind if there's an arms race going on.
Starcourt Industries (the owner of the mall) is described as an "International enterprise". That's their cover story.