No, the metric is not what one word ('engaging') tries to describe what it potentially is. If a reader is least interested, no metric can predict engagement. If an administrator's job is to configure the server, they will be super-engaged reading dull documentation! I can only think of casual communication (email, forum, StackExchange, etc.) where this particular metric will help. And yes, in many such instances it'll make the reading more engaging. In layman's term, I'd say Grammarly's metric will help not put readers to sleep.
On the official website they claim to add "vivid words" and to vary "the rhythm". The examples provided there makes sense from casual writing point of view. However, if someone is writing fiction, they'd have their own flair and style of writing. No rules or metric required there. On the other hand, in technical writing where superfluous words are anyway not used and there's a style guide to be adhered to, there's no room for vivid words and the metric doesn't apply.
To answer the other half, the metric is based on AI/ML algorithms. The content is processed probably using NLP techniques that try to give score to abstract things like emotion, sentiment, engagement, etc. related to some text. While the techniques are super helpful and are well-established, it is still man vs machine. The AI/ML algorithms have much to learn. Use the advice where it is helpful. Ignore the rest. Demand to train the algos better. The other comment mentioned manned aircraft example, that's concrete reason to ignore and move on to a human editor.