Smith assimilated every human in the Matrix, but that does not result in death for the assimilated human.
Smith's ability to assimilate people in the Matrix is derived from an Agent's ability to do so, except that Agents are limited to assimilating one individual at a time, whereas Smith can copy himself and in doing so assimilate multiple individuals simultaneously. Agents' assimilation ability restores the possessed individual if the Agent leaves that individual. Usually an Agent leaves the possessed body because the body has sustained a fatal injury (in which case the possessed individual obviously dies), but in some cases we see that the Agent leaves an uninjured body and the possessed individual is restored unharmed (albeit with some memory loss). For example, the comic "Wrong Number" demonstrates this:
It stands to reason that humans assimilated by Smith are similarly restored unharmed except for memory loss.
Furthermore, we see several programs which were assimilated by Smith but which were restored to their original form after he was defeated (e.g. the Oracle and Sati). Most conclusively, the fact that the humans in the Matrix are alive after Smith's defeat is made explicit in the final conversation between the Oracle and the Architect:
The Architect: Just how long do you think this peace is going to last?
The Oracle: As long as it can. What about the others?
The Architect: What others?
The Oracle: The ones that want out.
The Architect: Obviously they will be freed.
The Oracle: I have your word?
The Architect: What do you think I am? Human?
Note: the original version of the question asked if Smith killed everyone on Earth, not just in the Matrix. I've included the remainder of my original answer to that version for completeness.
Smith did not kill everyone on Earth. There were many humans still alive in Zion after Smith was defeated. In fact, it was because Smith was defeated that the Sentinel army was called off and ended its attack on Zion: Neo made a deal with Deus Ex Machina in which the Machines would end their attack on Zion if Neo defeated Smith:
Neo: The program Smith has grown beyond your control. Soon he will spread through this city, as he spread through the matrix. You cannot stop him. But I can.
Deus Ex Machina: We don't need you! We can stop him!
Neo: If that's true, then I've made a mistake, and you should kill me now.
Deus Ex Machina: What do you want?
The humans in Zion weren't plugged into the Matrix and hence were safe from Smith.