This was the Rockingham Railroad, later operated by the ACL which ran from Bennettsville, SC to Rockingham , NC thru the town of Gibson, NC. This segment was abandoned late fifties to very early sixties
I dont think the time frame for abandonment is correct. Early 80's Gibson Christmas Parade was interrupted by a train, I was in a Marching Band from nearby Laurinburg. Google shows the tracks maintained as of 2013.
The rail line you're looking at is the CSX Andrews subdivision. The Rockingham branch paralleled the old SAL main line a few hundred yards from the station north past a mill before turning back northwest in the middle of Gibson, NC. Abandon date would have happened no later than 1967 when the lines were merged to create the SCL railroad.
It has been an easy 30 plus years since I was in Gibson NC, so Im assuming you are correct. I only remember the 1 track in "downtown" It also seems like there was a "Firehouse" subs right beside/near the tracks. All of this brings back a ton of memories growing up!
The third and fourth quarter 2010 issues of Lines South published by the ACL and SAL Historical Society contain a two-part article by Michael J. Dunn on the Rockingham Railroad which operated under agreement with the ACL, the branch between Gibson, NC and Bennettsville, SC. The article contains information on the ACL line in addition to the Rockingham Railroad. According to the article, the portion between Gibson and Bennettsville was abandoned in June 1968 as no longer needed due to merger. There is a short segment of the line still in place - in use? - in Bennettsville where it connected to the line between Parkton, NC (south of Fayetteville)and Bennettsville that ended a short distance southwest of Bennettsville. This line is now operated by the shortline Pee Dee River Railroad in service between McColl, SC - connection to the ex-SAL Hamlet to Charleston "EC" line - and Bennettsville to the quarries to the southwest.