Why are they not a threat? They have a large nuclear arsenal and view the US as a threat. They were and still are concerned about the US trying to foster in Russia a "velvet revolution" like the ones in other former Soviet republics. Call it paranoia, but after a history of invasions and attempts, many in the Russian government see the US as ready to steal their oil and mineral wealth and eliminate Russia as competition.
I know it is a lot to ask someone to sit through propaganda videos, but did you watch any of the Big American Show videos I linked to? It makes 9/11 truthers and Loose Change look almost sane. According to the view preached to Russian citizens by their government, the US is responsible for every bad thing that has happened in the world in the past 100 years. WWI, WWII, killing people only for financial profit, deliberately inventing pop culture to get Russians and Europeans distracted from having children thus allowing immigrants to take over their cities, ordering terrorist attacks including 9/11 in order to control people with fear. "Who cares the towers were destroyed by soldiers? Who cares that there were no passengers on Boeing that crashed into Pentagon?" "[The US] made these countries (former Soviet republics) our colonies." "We (the US) need Ukraine to get closer to Russia (with a graphic showing a missile launched from Europe into Russia.) The US ordered Georgia to attack South Ossetia because McCain was behind in the polls. The economic crisis was orchestrated in order to make a profit for the rich (like Bush) and allow Obama to control people with fear of poverty.
Any country with such a negative perception of America, feeling so persecuted and actively spreading that message to its youth to believe, sees America as a threat and a rival.
Are they an economic threat? No. A threat for a a Red Dawn style paratroop invasion? No. But they still have nuclear weapons and view the US as a threat to them. I would agree the threat is less now than in the 1980's, but argue it is higher than when Yeltsin was in power.