I don't recall a red Briggs in that period, so I suspect it has been repainted. It is not the original engine in any case: you have a single deck SB45, which means it is quite an early one, late 1960s to early 1970s, but that engine was made on the 14th of May, 1980. It has a cylindrical air cleaner, which AFAIK was only applicable to the heavy duty air cleaner, which had a pre-filter around the outside of the paper filter. The normal flat Briggs filter is single stage, using a foam element. So, at this point we don't know whether it originally had a Kirby Lauson or a Briggs engine, and we can't tell the date of manufacture of the mower except that it is an early one.

The Briggs 60102 was actually fitted to some early SB45s, though I can't recall one with that air cleaner. The ones I have seen were advertised as 2 hp. They had a Vacu-Jet carburetor The 60202, which came to SB45s slightly later, was advertised as 2.5 hp. It had a Pulsa-Jet carburetor.

Here is the Operator's Manual for your engine:
http://bsintek.basco.com/BriggsDocumentDisplay/lrvvA-wU7eL7hAxB91ObQ.pdf

Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/18lowGXBnfBhU7y.pdf

I'll leave Deejay to comment on the mower itself - I think he will be able to find some clues as to when it was made because of running changes that were made in some of the details. It looks to have been badly repainted, but otherwise looks promising to me. Could you add a picture or two of the chains and sprockets, though?