Is throwing a soap bottle at someone's direction considered as some type of assault even though the person wasn't hit directly?

State statutes can define assault differently, but the general rule is assault is the threat to harm, and battery is the actual harm. 

Your scenario is no different than if you point a gun at someone, pull the trigger, and miss. That is certainly still a crime. The charges would be more serious, but the scenario is the same. 

"Hit directly"?

Is the bottle okay?

Yes. You don't have to make contact for an assault to occur.

At least it was a clean fight .

The THREAT of throwing it is assault by the traditional definition. Actually hitting the person is battery.

It can be, yes.

It's almost to the point now where giving someone a dirty look is considered assault.

Well, it's an act of violence.

intent rather than incompetence