I think that's what they used, in the screenshot you can see flashplayer_32_sa.
You are correct. It took me so long to find it that I forgot to check to see if the name matched and I just posted the link.
That said, I did find out that you have to hack flashplayer_32_sa.exe a bit if you want it to be able to open .SWF files properly by clicking on them.
You'll need a hex editor that can edit Unicode text (I used the
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), do a search for the Unicode string "-relaunched" (or just go to offset 9AAF2C), replace that whole string with Unicode spaces (hex: 20 00), and then save it. Now you can right-click on a .SWF file, choose "Open with" -> "Choose default program...", click "Browse...", select your edited version of flashplayer_32_sa.exe, click "OK", make sure that "Always use the selected program to open this kind of file" is checked, then click "OK" again. Now you should be able to double-click any .SWF files and it will open them "instantly".
Apparently this has been broken since v24. They're up to v32 and still haven't fixed it.