Does Tessie die or are they just throwing stones?

Tessie definitely dies at the end of "The Lottery." The villagers aren't just playing games.
The story offers many hints that show this truly is a lethal lottery. First, we learn that the village boys made "a great pile of stones in one corner of the square." They are completely serious about the stoning.
Second, there's a general sense of nervousness and unease about the lottery, and Mrs. Adams makes the statement that some villages have quit their lotteries: her statement suggests this is more than just a stone-throwing game but is instead a barbaric ritual that ought to be abandoned.
Tessie also wouldn't protest so repeatedly that it isn't fair if she knew she wouldn't be killed. Finally, the killing nature of this lottery becomes apparent when

Delacroix selected a stone so large she had to pick it up with both hands.

We learn, too, that

A stone hit her [Tessie] on the side of the head. Old Man Warner was saying, "Come on, come on, everyone" . . . and then they were upon her.

A savage mob mentality takes over as the crowd releases its aggressions on Tessie.