Are there any examples of European rulers with a rank lower than king to utilize a "throne" and a "throne room"?

The answer to the question is really subjective and depends on what we consider a throne and throne room.

To illustrate this on an example from the middle ages: the Republic of Venice and the Doge (elected ruler). The Doge's Palace has a Council room (Hall of the Great Council, Sala del Maggior Consiglio) that was the center of all political decisions and was designed for about 2000 citizens plus Doge and officials. The seat in this room clearly has a similar function that you described as the throne room. Is it? In the same building, there is Sala del Collegio, the room where the Cabinet and the Doge were meeting, and also for meeting important foreign visitors. The chair of the Doge is explicitly called a throne in the description, and the room also had the function that what you would call a throne room.

Now let's walk to another building in the same city: MUVE, originally a palace one of the old, wealthy families (Bon). If you take a look at the layout, one room is called the throne room. To be fair, it was named after a very important chair used by a pope. My point is: the rich and influential often had a designated room, home office space, to meet with others, and that room generally had chairs, some of them even pretty big, to represent power (see a list at Wikipedia).

References:

• https://www.planetware.com/venice/doges-palace-i-vn-vd.htm
• https://carezzonico.visitmuve.it/en/il-museo/museum/building-and-history/
• https://en.wikipedia.org/wiki/Throne

This isn't a rigorously structured question, so I'm going to give an answer with less rigor than I generally prefer.

1. There is no enforcing body. There exists no police force who will come in and reclassify your throne as "merely a fancy chair". So I think it is entirely plausible for your count to be the only person seated in the room on a chair that demonstrates conspicuous consumption, is elevated above the floor, etc. I have no doubt that some of the people in that room will use the term "throne", but everyone in the room will understand the message.

2. The particulars vary significantly through history, but in almost all cases, the senior person in the room must do something to be set apart. I can't find a succinct summary or quote (I welcome edits/adds), but this is part of the reason for customs such as waiting for the host to sit before you sit – sitting first implies precedence. If there is only one chair in the room, it is reserved for the senior person (and therefore it is 'a throne' even if nobody uses the specific term for it).

3. Again, the particulars vary in time and space, but authority generally needs a symbol to convey that they are acting officially. The authority seated in a room full of standing subordinates is sending a message.

4. "A throne is the seat of state of a potentate or dignitary, especially the seat occupied by a sovereign on state occasions; or the seat occupied by a pope or bishop on ceremonial occasions." Wikipedia

5. Some other prelates besides bishops are permitted the use of thrones, such as abbots and abbesses. Wikipedia

6. Design Institute of San Diego has a short article on the use of the chair through history.

7. Although it is quite outside the time and boundary of your question, it may be useful to consider the role of the stool in some African cultures.

Out of time – I hope that helps at least a little bit.

For the actual 'room' the term Throne room seems to be well established:

throne room or throne hall is the room, often rather a hall, in the official residence of the crown, either a palace or a fortified castle, where the throne of a senior figure (usually a monarch) is set up with elaborate pomp—usually raised, often with steps, and under a canopy, both of which are part of the original notion of the Greek word thronos.

On that page we see examples for lower-than-kings, like Monaco.

A problem with this concept is that in Europe most smaller rulers of that timeframe in most of Europe had to represent their power and money and whatnot with this kind of architecture. But these rather large rooms or halls were not necessarily really where such rulers actually sat all day to — well, rule from the stool all the time? Such accommodations were of course used for audiences, ceremonies, festivities, honours, assemblies of court etc.

One such example of a throne —without a throne room!— would be the Duke's chair in Carinthia in use from 1161 to 1597, similar in function to the Coronation Chair. Obviously, taking power was symbolised by taking seat on that seat, but everyday business was then conducted elsewhere afterwards.

We therefore need perhaps look at the functional aspects of 'a throne room' which are transferable to other rooms and contexts, and therefore give rise to a lot of other names for such a room. The idea that historical monarchs in particular performed almost all of their official functions in a throne room is likely to be a romanticisation in most cases. Many monarchies in the early historical period of inquiry here were operating without having even a proper capital or a residence.

If we consider these differences, then we might discover still quite a lot of examples like in Meißen the Albrechtsburg with its "Great Hall", which was built from 10th century by Margraves and taking its present day appearance in late 15th century under Electors. Similarly, the Dresden Castle features two rooms called properly 'Eckparadesaal' and 'Audienzsaal', although they are alternatively called throne room and new throne room, for the Elector of Saxony, after their apparent functions.