Sorry for being a pain, but I like to be precise. So I went to the video again, screen dumped the letter/envelope image, and did some measurements myself.
The envelope does look like a 'normal' one based on the proportions, not a card envelope.
US Envelope Sizes Including Commercial, Announcement & Catalog Sizes
I make the assumption that it is a size 7 width 3.75", as that is a close fit in proportion.
Based on the envelope width, the letter size is about 7 3/4 by 4 5/8", perhaps a bit wider because it looks curled.
7 3/4 ÷ 2 = 3 7/8, which is 1/8" longer than the envelope width.
It is then up to interpretation, whether it can still fit into the envelope being about 1/8" wider with one crease!
Please let me know if measurements were different in 70's, I can fine tune it.