Web design entails the creation of web sites, and as the tools of the trade have become more complex and the demands of the web populace have gotten stronger, web design has become closely akin, if not the same as, SoftwareDesign. Modern software commonly employs methods of connecting to other applications over the net, so much so that the boundaries between software design and web design have become blurred. A fair prediction is in the near future these two aspects of computer programming and publishing will be unified under the same category.
However, designing presentations for a web interface remains something of an art as opposed to strictly a science. This is not only for the technical reasons having to do with browser compliance to various standards, but also to the restrictions of dealing with a variable viewport, user-determined styles, user-determined color settings, etc. Modern web interface design is no longer one lone geek plugging away at HTML in his basement. Properly designed web applications require a cross-pollenated understanding of all the pertinent characteristics of a user's environment acting together. Therefore, it is highly unlikely that web design as a specific skill set will disappear any time in the near future.
I don't think we need this category. We already have CategoryUserInterface and CategoryInternet. We cannot create a category for every existing combination of such things.
I did not create this category. I think the person wanted a category for pages related to developing applications for the web. If that is the case, then I see this category has a different purpose than the ones you have mentioned.
In general I think Internet-related categories perhaps need a rework. But perfect categories are hard in a changing world.