Every outpost of the empire will essentially have unlimited manufacturing capability and it will take decades to project force, decades the outpost can spend making sure the amount of matter they have devoted to war exceeds the tiny amount of war matter the central empire threw out into space.
The big idea of the book is that Einstein isn't wrong about C being the speed limit. Therefore, to be a starfaring race requires the ability to make commitments and hold to them over extremely long timespans. The connection to game theory is that, as in the Prisoner's Dilemma, the only way you can really make predictably right decisions in cooperation with other entities is if your decision-making formulas are spelled out mathematically in advance; so all can predict how you will act. The first book begins with mankind discovering the galaxy's "rules" on a kind of signpost at a nearby star.
Read the books!
My point is that the very concept of an interstellar resource war, and thus the concept of interstellar control, is incoherent given our present physics. You can take over a system that isn't technologically enabled, but that's it, the resources available to a technologically enabled system are greater than the resources that can be sent into the system.
So it's certainly feasible for an advanced race to build a star empire; the question is why they'd want to do it. If we're talking about humans you might say ambition or imagination. If Vulcans, maybe they'd think it logical to pre-emptively become stronger than any potential aggressors.
You could slam a bunch of mass into a system at extreme speeds, but then they just have to hop into life boats until the storm ends (if they have the capacity to ponder traveling the stars, they have the capacity to spend a decade on a space station).