The Space Race is still happening, but it's happening on other planets and with government money (see: Mars and further afield exploration). All these initiatives have been possible by the heavy lifting of NASA and other international government agencies over the last 6 decades.

Theses newcomers have drawn in attention and effort and are trying to reframe space as a business being funded by revenue - which has trade offs but in general is a positive development. The really challenging work without the glamor is still being down by the scientists and research agencies with the government. I do tip my hats to the accomplishments of all three of the new comer organizations. I just dispute that the narrative that they are driving the future. I think they are complementary.

To be clear - they don't have enough money to "solve" space exploration - it takes deeper capital than they have - though they are bringing a new business model to potentially stretch their capital deployments.