They're expressing a preference for who winds up in the Cabinet, yes. There's no indication in that transcript they have anything other than diplomatic pressure and persuasion to make that preference a reality. Note phrashing like "I think your argument to him, which you'll need to make".

The Russians will have had their corresponding preferences and influence campaigns, just as they did in US elections. (They may have even expressed them via dioxin, in Yushchenko's case.)