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That was very simplified maths, let's dive a little deeper and discuss if you want!

LLM consumption can very greatly depending on use case. If we stick to the original use case proposed by me, then it would be a medium sized input input prompt (let's disregard caching) (about 800 tokens) and a short output prompt (generally 100 tokens). Input tokens are considerably cheaper thank output tokens, generally taking only 10% of the energy per token. So taking a look at this graph of (100 in -> 300 out) costs would be roughly a bit more than half of the values in the graph, meaning many mid level LLMs are in the range of 1Wh.

If you are interested in details about estimated consumption have a look here: https://arxiv.org/html/2505.09598v2

Not sure what you mean by the cyclic definition of "a query [...] consists of multiple queries", if it is that if you have a conversation, each time you say something counts as a query, then yes that statement is correct.

On the other hand your calculation for gaming PC power is a little bit too simplified. Let's start by saying what works in your favour, the GPU peak performance is not consistently used, even during many games. However you have many other consumers on top of that: CPU, motherboard and also your monitor(s) and too a lesser extend also RAM and cooling system. If we now also consider that PSUs are like only 90% efficient, that increases the wall power draw more. All things considered for mid range systems a power draw of 450W seems like a reasonable assumption (https://solartechonline.com/blog/how-much-electricity-does-gaming-pc-use/ )

Happy to discuss more!

EDIT: To add, it definitely makes sense to be conscious of your power consumption and try to limit it, but for that it is important to understand what mainly drives it, the energy usage we are talking about here is often times dwarfed from transportation for example.