The figurine of wondrous power is a magic item, and therefore by the definition in the SAC, magical in a game-mechanical sense, i.e. activating it would not work in an antimagic field, detect magic would detect it, etc. It says
If you use an action to speak the command word and throw the figurine to a point on the ground within 60 feet of you, the figurine be comes a living creature. (...) The creature is friendly to you and your companions.
It understands your languages and obeys your spoken commands. If you issue no commands, the creature defends itself but takes no other actions. See the Monster Manual for the creature's statistics, except for the giant fly.
The creature exists for a duration specific to each figurine. At the end of the duration, the creature reverts to its figurine form. It reverts to a figurine early if it drops to 0 hit points or if you use an action to speak the command word again while touching it.
What about the creature that is created once the figurine is activated. For example, the Onyx Dog. Would it still count as a magic item, and would its attacks therefore count as magical attacks?