This is another one of the those terrific questions, where most of the research is already done in the question
The claim I am addressing is: Was Marilyn Monroe was much larger a modern size 12, the same as a modern size 12, or smaller than a modern size 12?
Some people claim she was large, including Roseanne Bar:
"I'm more sexy than Pamela Lee or whoever else they've got out [in Hollywood] these days. Marilyn Monroe was a Size 16. That says it all."
[Source: The Phoenix Gazette. "Say What?" 23 February 1996, via Snopes]
Barr is not a reliable authority and I haven't found any real evidence of this.
The link you gave claims she was a size 12.
However, dress sizes are poorly standardized and have changed over time (Ref). A size 12 in the 1940-50s has become a size 6 now (Ref). So this information isn't very helpful.
But, in fact we have evidence that she was smaller than a modern size 12.
US catalog sizes put modern day Size 12 as roughly:
Est. weight 155lb (70kg)
Your own source, quoting from a biography, has two sources for Monroe's measurements:
(studio's claim): 37-23-36 (inches)
(dressmaker's claim): 35-22-35 (inches)
Both of those are considerably smaller than a modern size 12. Those dimensions don't particular fit any of the US catalog sizes (and I am sure many women would attest that is also their experience.)
It also puts her weight at:
118 pounds 53.5 kilograms
which is under the Size 12 estimate. (I acknowledge that stating someone's general weight to within half-a-kilo is a overly precise.)
Furthermore, we have experimental evidence:
Here is a quote from a fashion writer, Sarah Buys
Contrary to received wisdom, she was not a voluptuous size 16 — quite the opposite. While she was undeniably voluptuous — in possession of an ample bosom and a bottom that would look at home gyrating in a J-Lo video — for most of the early part of her career, she was a size 8 and even in her plumper stages, was no more than a 10. I can tell you this from experience because a few weeks ago, I tried to try on her clothes.
Source: "Was Marilyn Monroe a Size 16?" The [London] Times, 11 April 2009, via Snopes
Marilyn Monroe was smaller than a modern size 12.
Asking what size she actually was makes too many assumptions to answer: i.e. that dress sizes are well-standardized, human dimensions can be fit into a single scale, and they are stable.