The PDP-6 multiprocessingmultiprogramming monitor, an early operating system first delivered in 1964, used the term "filename extension" for the second name attached to a file, usually indicating the type. It also used the dot character as preceding the extension.
The linked document explains the monitor, although not in detail.
Multiprogrammed monitor
In that document, under FILE DELIMITERS, you'll see that dot precedes a filename extension.
The people who built the monitor were undoubtedly influenced by the CTSS system at MIT. Some of the early PDP-6 team were veterans of the Tech Model Railroad Club, and had persuaded the designers to add four stack oriented instructions to the repertoire.
Edit: The PDP-10 was a follow-on processor to the PDP-6, and the monitor added support for it. Eventually, the monitor was renamed to TOPS-10. The dot convention spread to the other operating systems within DEC. CP/M and MS-DOS also used the dot to separate the two parts of a filename.
Bill Gates may have first been exposed to the filename.ext convention when he worked on a PDP-8 in prep school.