The plan intrigues me on a number of levels. Firstly it appears to face one way ie. in favour of traffic travelling to and from Bristol rather than to or from London. This doesn't appear to make sense, not only for this reason but also because it appears to ignore the existence of Malmesbury, Tetbury and surrounding areas.
It is also a pity that the map (or the others in that series) doesn't show Wootton Bassett, because to me the M4 route appears to be aiming closer to that town than where it was actually built. I know that the original plans were amended in the mid 1960s to send it a bit further north due to the (then) planned housing development between Wootton Bassett High Street and Coped Hall roundabout, that the M4 would otherwise have gone straight through, and if it was shown that would have helped to date the plan.
However...
The M4 was opened in stages. The first section to open was from Chiswick to Maidenhead between 1961 and 1965 (which is, incidentally, why you have junction 8/9 - the original junction 9 was at the end of the motorway where it joins the A4 to the west of Maidenhead and is now part of the A404). Parts were built in South Wales and the Severn Bridge was opened in 1966. From 1966 to 1971 there was a whopping great gap in the road between junction 18 at Tormarton and junction 8 at Maidenhead, and traffic had to go south on the A46 to Cold Ashton (roundabout now, lights then) and carry on along the A4 to and from Maidenhead.
I very much suspect that this spur was proposed as a temporary measure to slightly reduce the distance, and reduce the congestion at the Cold Ashton lights. The fact that it would have been of limited use once the M4 had opened throughout would explain why the decision was taken not to build it at all.
The timeline for all this is here:
https://en.wikipedia.org/wiki/M4_motorwayps - when I as about 13 I rode my push bike down the M4 adjacent to Westerleigh Yard when the motorway was still under construction...