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
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?