You're limiting the definition of democracy to 100% pure direct democracy i.e. literal mob rule. I struggle to imagine what such a government would even look like (on a large scale, at least).

I tend to think of a republic as opposed to a principality (it's right there in the name, even!). That is, the machine of government is thought to be held publicly rather than privately, in a republic. Suffrage has nothing to do with it, although democracy is a common implementation of a republic. (Other examples might be a military government, a religious oligarchy, or a corporate oligarchy). It is a rather broad term.

Constraining what the citizens are allowed to do, or how they are allowed to do it, via fair voting representation in their government (that is to say, limiting the powers of their duly-elected government by a constitution) does not to my mind diminish the fact that it is a democracy. Nor does it diminish if they elect representatives rather than participating in endless referendums.

My thinking on this seems clear and objective enough to me.