Your are confusing yourself with your analogy, brains are not like computers. The complexity of the "software" a brain can have is determined by how many cells and therefore connections it can have. In particular flexible (learned) thinking as opposed to instinctual "programs." Brains that are flexible need more cells to allow for more possible connections. Computers are not great analogies for brains they are just the best we have. but to use them a brain is like a solid block of ram, yes a large mass is not necessarily fast but it Can do a a far larger variety of tasks, intelligence is not a measure of speed (flies react way way faster than humans) but generally a measure of how many things you can be computing at the same time. the human brain is basically built to model the entire worlds around us including the brains of other humans, which is many many tasks happening simultaneously. Which is one reason brain size can also be used to predict how social an organism is, (at least in non-kin selected social behavior) social interaction requires modeling many complex things. You also run into the problem with defining intelligence, which is problematic to say the least.
And as another poster has pointed out natural selection will quickly eliminate unused brain mass, (neurons are super expensive to maintain, our brain eats about a third of the calories we consume) so they are strongly optimized for weight, so portions of the brain that are larger should, in general, be doing more to offset the cost, otherwise they will be quickly shrunk. So a portion of the brain that is large must be being used, and must be offsetting the caloric cost, also note many the parts of the brain are fairly basal to the groups being compared like mammals so the so the chances of drastically different fundamental ways of operating are fairly slim. so if the same portion of the brain is very different in size between two related organisms chances are it is becasue that portion is doing more or less. It is even easier to see with sensory processing portions of the brain, if the olfactory bulb of the brain is huge it has to be due to an increased function in the the sense of smell because it really doesn't do anything else and how the sense functions has not changed. this is backed up by observation the brains of animals with poor senses of smell (like cetaceans) have tiny olfactory bulbs while animals with excellent senses of smell (blood hounds)have huge ones. Intelligence is associated with enlargement and complexity only in specific portions of the brain, not the brain as a whole.
That said brain mass is only a rough estimation. It more done to control for body mass (which effects brain mass directly) as things like how folded the brain is can drastically alter the complexity without changing the mass much. No one assumes brain size is a prefect predictor for intelligence.