I think you are a little unfair in your comparison of bitcoin and gold. Gold has advantages over bitcoin, but bitcoin also has advantages over gold. Storing gold is more expensive then storing bitcoin. Transacting gold is much more difficult than transacting bitcoin. One of the downsides of bitcoin is that it could go to zero for some reason. I think gold has less of a risk of that, but other investments have a significant risk of going to zero.

I am not sure I understand the negative sum game you mention. The first payment miners get is (I don't know the proper name) a bounty, which is equivalent to a gold miner obtaining gold. This can be seen as a built-in inflation, which not only gold but also any fiat currency has. The difference is there is no known limit on this inflation factor for gold or fiat currencies. For gold we assume some gargantuan deposit will not be found and that it will maintain its scarcity. I don't think anyone thinks there is an inflation limit for the US dollar or any other fiat currency. Bitcoin has a known amount limit. (As a disclosure, I own gold, bitcoin, and US dollars.)

The other part of what miners make is a transaction payment. That exists in every other payment system I assume, except I guess physically handing an object to another person, which covers a pretty small fraction of transactions.