"This isn't something serious, just nationalism and/or cronyism. A real domestic processor project? It wouldn't be "dozens of millions of dollars" it would be tens of billions. Intel spent $10 billion on R&D... in 2013 alone. TSMC, who's just a fab not a designer, spent $1.4 billion in 2013."
I won't dispute your figures, but I do find them on the high side.
First, the budget for such a project doesn't need to be spent in one-go. The project can be developed in stages with the money spent being increased as each milestone is reached.
Second, the CPU's don't need to be bleeding-edge. The article already stated that an existing design will be (re)used, so the budget for research is going to be drastically reduced. Consequently, Russia can simply import the parts for a fab that's one or even two generation behind the latest process, again resulting in signifcant cost savings.