Alexander is talking about 'spaces' in buildings, how they take shape, how they interact, and how they serve the greater style and purpose intended by the master architect to serve the lifestyle of the resident. Here design focuses on the end product and how it will function for the user. These design patterns have nothing to do with how the building was constructed or the experience of the tradesmen who built it.
In contrast, the GoF book did not talk at all about the final software end product, but only the process of building it. The emphasis is entirely on the tools of the tradesmen and encouraging their proper use and re-use. Such design patterns do not reflect the user requirements or even the architect's high level design of the software product, much less serving the user experience in a consistent purposeful way.
However it seems to me that Alexander's approach to patterns could have been adopted in the software domain, but I think that would have looked a lot more like Jef Raskin's style guide at Apple which encouraged developers to adopt a common holistic yet systematic approach to Mac software so that the user experience was served. I think Raskin wanted apps to fit together the way that rooms in a well designed house flow from one to the next -- something Alexander would endorse, I think.
Another variant on design patterns in the software that might have worked well, at a level that might have bridged Raskin to the GoF, could have been Alan Kay's model for objects. The higher level conventions for components and behaviors that Kay espoused might have made for an interesting basis for patterns like those of the GoF. But without Kay, much less Raskin, the very modest ambitions of today's notion of software design patterns led nowhere but software reuse -- an inauspicious end to Alexander's vision, IMHO.