The USSR collapsed in 1991.
I believe the author meant the drillbook such as https://issuu.com/normagee/docs/scanavi_sbornik_konkursnih_z....
The first manned US flight was a month after the Soviet one, and the US had successfully returned monkeys from space before that, so arguably they were ahead technologically but less willing to use a human test subject.
It's more accurate to say that ICBM development in both the US and USSR had the unintended side-effect of giving birth to human space travel once the political benefits of using nuclear launch systems for human space travel were realized.
Uncontrolled military spending is a funny thing.