Interesting question, the alternative OS would have had to have had a good leader and I am sure maybe RMS would have created a kernel after some time.
Maybe somebody would have taken 386BSD/FreeBSD/NetBSD and made something completely different.
I think another question would be, if Linux was never invented, what technologies would never have happened. For instance, a bunch of animation movies where made with Linux farms, Planes use Linux within their inbuilt entertainment systems, the list goes on (I think NASA uses linux on their ISS). How many people would be interested in technology/IT sector, how many companies would have started (ie: RedHat, Thwat,etc), What features/addons would not have been added to other operating systems (Windows tcp/ip)? Would docker even be a thing, hyper-v ?
I know one thing....... All the old technology would be alot more and schools would have alot more vunerabilites on their PC's.