Well, I do use fossil fuels in various ways (I have a car, I have a heated home, and I consume electricity which is approx. half fossil locally) - and yes, I do not consider continuing to do so unethical. It would be preferable to use less fossil fuels, which is a consideration for me, but I definitely do not consider that there's an ethical duty for me to use zero fossil fuels.

While we can (and should!) agitate for policy changes to reduce fossil fuel usage, it's appropriate to request that, I do not consider that it would be ethically appropriate for me or you to demand total "fossil abstinence" from any person around us - freedom and respecting others' freedom is also a valid ethical value, and actually imposing your will on others requires substantial justification, and having ethical ends do not imply all means would be ethical.

You could s/play video games/ with a whole plethora of morally objectionable strings but that doesn’t make it equivalent to playing computer games.

Is it ethical to pay taxes to a government that does unethical things?

Yes, if it's used in efforts to combat climate change, e.g. powering alternative energy research, or attending climate change conferences, etc.

It might not be an easy way to avoid using coal electricity.

Not buying a game in game saturated market is not that hard or essential to quality of life