The owner of Platinum Emperion will lose because Smash to Smithereens is a multi-step spell. The Emperion is destroyed before the damage is dealt:
608.2c The controller of the spell or ability follows its instructions in the order written.
The Emperion ability stops functioning as soon as it leaves the battlefield:
611.3. A continuous effect may be generated by the static ability of an object.
611.3b The effect applies at all times that the permanent generating it is on the battlefield or the object generating it is in the appropriate zone.
And, importantly, "destroy" causes the Emperion to leave the battlefield immediately (as opposed dealing it lethal damage, which would not cause it to die until after the spell had finished resolving because that is when state-based actions are next checked):
701.7a To destroy a permanent, move it from the battlefield to its owner's graveyard.