While it might be helpful to know some HTML, most of the time, an embedded developer (just as an example) will not need that knowledge, not hone it and, as a result, not be able to use it either way. It's the same for other types of software engineers. There are some rather theoretical architects, there are low-level developers (OS, drivers, etc.), there are desktop application developers and last but not least specialized app developers. Web dev is a nice-to-have, but should they know it? I don't think so and I would never require them to.

No, many software engineers don't touch the web. Things like programming embedded microprocessors, building operating systems, writing compilers, data mining, AI, integrating into banks, writing software that controls planes / cars, realtime software, software written in ADA for example that deals with very critical things like manned space travel or even nuclear power stations, robotics, 3D vision applications doesn't require web and even mobile and desktop applications doesn't require web if you're building native applications

Web is a nice-to-have skill, although very in demand skill if you don't have any of the other specialities

Basics yes. Even if they never write production HTML/CSS/JS they should have a broad idea how they work. Pretty much all roles on a dev team should have at least a conceptual understanding of what their coworkers are doing.

Voted for yes.

Knowing about web development will definitely be useful for a software engineer. For as little as creating your online portfolio basic knowledge of HMTL/CSS and JS is needed.

Like almost everything in programming, it really depends on the specific niche you want to specialise. Marco Alka and Jan Vladimir Mostert gave great answers, explaining that you can do just fine and be a solid developer without knowing HTML, CSS or JavaScript.

Web development is nice-to-have, but not mandatory.