The 1/7 GDP figure is misleading. It is absolutely true that everyone had an incentive back then to overstate the USSR's position: Communists and sympathizers for ego gratification, American liberals to use as an argument for government intervention in the economy and internal reform, and the American Right to ramp up militarism and domestic repression. That said, the revisionism that argues that it had no more power on the world stage than South Africa based on spurious GDP comparisons is just as off base.
GDP captures something meaningful, but in terms of ability to project power it's only somewhat correlated. In a Communist state, it captures even less, because pricing mechanisms are all off kilter.
For much of the USSR's post WW2 existence, it could likely have invaded and taken much of continental Europe using only conventional weapons. The USA had troops stationed in Germany not in hopes of stopping any invasion, but to buy a little bit of time and to make its defensive pledges plausible to allies: thousands of American dead would mean it would have to join in a total war, instead of calculating costs and benefits of total war (which would be unacceptable). Even then, other counties worried about America's commitment to an incredibly costly war with the USSR: that's part of why France developed its own nuclear deterrent and left NATO.
Discussion of whether the USA or USSR would "win" an all out war between them is almost besides the point: they both possessed enough military power that the only way to win would be to, um, not to play.