Searing Blaze has two targets. It targets a player and a creature that player controls. This is true regardless of whether or not its controller has landfall. With Landfall, the only thing that changes is the amount of damage that is dealt to the two targets.
In order to cast Searing Blaze, you must be able to choose both legal targets. If a player cannot be targeted or a player can be but he controls no creatures, then you cannot play Searing Blaze.
Searing Blaze will not become countered on resolution unless both of its targets are illegal when it attempts to resolve. If at least one of those targets are legal, then Searing Blaze will resolve and do as much as possible. In other words it will deal damage to the targeted creature or player that is still a legal target.
Today’s Rules Tip was suggested by Steve Peterman, a level 1 judge from Minneapolis, Minnesota, United States.