The speaker spends the morning pretending to be someone important: an "old head" crammed with business, the kind of person who has deals and decisions on their mind. The title, "Tycoon," sets up that image of a powerful, self-satisfied man. But the second stanza undercuts it. The speaker admits they are "in no mind to play" this role, and then, bluntly, names what they really are: a "fat rat."
That last phrase is the punch of the poem. A rat is scavenging and low, and "fat" suggests it has grown comfortable by feeding on whatever it finds. The speaker seems to see through their own act, and the self-judgment is harsh and a little funny. The mood is dry and wry, with an undertone of weariness or self-disgust. The short lines give it a quick, blunt feel, like a thought that slips out before the speaker can soften it. It leaves you wondering how much of the "tycoon" is costume, and how much of the rat is honesty.