No. требует is sing., so it refers to Чечня. которые is acc. pl. then. тех means тех денег.
Moscow hates to part with money. But not with the money Chechnya demands for their pipeline, but with absolutely other money. (which would be demanded by other regions)
Aha, ясно. So, Moscow is in principle willing to pay Chechnya a fee for pipeline-use (in a strictly bilateral agreement with Chechnya, and only with Chechnya) but does not want to "create a legal precedent" that would encourage other regions to demand a fee.