Can a new company make a processor compatible with Windows and current software?
In theory a new microprocessor manufacturer could enter the market. In practice this is very unlikely, but not for any reason to do with the x86 architecture - the barrier is economics.

Manufacturing modern microprocessors is a highly complex engineering challenge which requires a lot of very expensive equipment. Getting the design right in the first place requires a massive upfront investment. And the profit margin on each unit is tiny, so in order to turn a profit you also have the additional overhead of investing in automation - you cannot just employ an army of production line staff.

A saturated market place with established players, high fixed costs and low profit margins is not going to be attractive to start-ups or new entrants, or to their investors.

The one thing that might change this is a breakthrough in technology. If you invent a way to manufacture a portable quantum computer from household waste in your garage using a few DIY tools, then you are home and dry.