Has your manager ever built a web app themselves? I find that this is a fairly important characteristic for a manager to have. The same way a junior doctor will report to a doctor who has been through the process of being a junior doctor themselves, or a teacher will report to a head teacher who themselves has been a teacher, a software developer should report to someone who has been through that process themselves.

Obviously, in small teams (for example, a small design house that does web development on the side), an engineering manager might not be strictly necessary. This works well where managers do understand the need to defer decisions to the programmers where necessary. However, as soon as things scale up, there needs to be structure.

Decisions such as who to hire, who to fire, how to address technical debt, which elements need most focus, and so on, need to be taken by developers; in addition to this, they sometimes mustn't be taken democratically because doing so would result in design by committee. In this instance, an engineering manager is required.

In large scale teams, there should always be a developer who spends more than 90% of their time not writing code.

I will take this a step further; a web engineering manager shouldn't just have a technical background, they should have a web background. Developing a Java application developer can be wholly different to building a PHP web application, and such an engineering manager should accordingly have an understanding of such a discipline by having some web experience (though it doesn't necessarily have to be in one particular language).