There is an explicit comparison near the beginning of ch. 21:
I wondered why the titans had not attacked Russia first; Stalinism
seemed tailormade for them. On second thought, I wondered if they had.
On third thought I wondered what difference it would make; the people
behind the Curtain had had their minds enslaved and parasites riding
them for three generations. There might not be two kopeks difference
between a commissar with a slug and a commissar without a slug.
There would be one change: their intermittent purges would take a
different form; a "deviationist" would be "liquidated" by plastering a
titan on his neck. It wouldn't be necessary to send him to the gas
chamber.
There are two editions of the book, one shorter and one longer. The shorter one has a shorter version of this passage.
Just because the first-person narrator makes the analogy explicit on one page of the book, that doesn't mean that the only possible way to read the book is as a roman a clef for the cold war. It's basically an exciting spy story, more focused on action-adventure than ideas. Nor would it be correct to portray Heinlein as a one-dimensional Cold War hawk. See How anticommunist was Robert Heinlein?