I don't know why. VMS also used it to indicate the revision number of a file, as I recall--demo.c.1, demo.c.2 ...--but it has been a while.
Years ago I worked with Data General minis. The 16-bit ones ran the operating system RDOS (real-time disk operating system), the 32-bit ones AOS/VS (advanced operating system with virtual storage. All used the '.' to mark of stem from extension, but all also had a file type associated in the directory. This meant, among other things, the the assembler would balk at processing something called urgent.asm if the directory showed that it was a generic file. That was baffling the first time you encountered it.
VMS also used the semicolon to do version information if you're interfacing with DCL or DECWindows (or NFS I think too). The dot was also used as the directory separator.
In VMS land your path would look something like (in the case of my login.com): DSA0:[USERS.MVEETY]LOGIN.COM;5
Unix has no concept of file extension. The dot is just like any other constituent character. To distinguish between file types, Unix uses the file(1) command and its database of manually curated magic strings and heuristics.
> Why is the dot/period character used as file extension separator?
Why not? Maybe it was realized that other candidate non-alphabetic symbols were already reserved for other things, like '/' as a path delimiter on Unices, '\' same purpose on Windows, '#' as a comment delimiter, '%' as the modulo operator, '|' as the command pipe symbol, '^' to signify either power or exclusive-or depending on context ... we're quickly running out of candidate symbols on an ASCII keyboard.
Windows/MS-DOS had file extensions (which it inherited from CP/M) before it had directories and directory separators.
Did CP/M and Unix independently come up with file extensions with a dot separator, or did they acquire it from the same source? I'm dimly aware of other operating systems that use(d) a different character (AS/400?), but it's outside my ken.
I believe Microsoft's file extensions and the 8.3 naming scheme are descended from Digital's 6.3 naming in VMS, RT-11, etc. DEC even used a number of the same extensions: EXE, COM, OBJ. Not sure where they came from prior to that. I don't think IBM used file extensions like that in System/360, System/32, or anything prior to PC-DOS. From what I can tell, Burroughs and Univac didn't use them either.
Years ago I worked with Data General minis. The 16-bit ones ran the operating system RDOS (real-time disk operating system), the 32-bit ones AOS/VS (advanced operating system with virtual storage. All used the '.' to mark of stem from extension, but all also had a file type associated in the directory. This meant, among other things, the the assembler would balk at processing something called urgent.asm if the directory showed that it was a generic file. That was baffling the first time you encountered it.