Read the dictionary entry

Spite (n): petty, malicious, or small-minded desire to harm or humiliate
In which sentence is the word spite used as a noun
The two old neighbors Continuously spy each other with their gaudy yard displays.
The runner Completed several yard victory lapse to spite his opponents. I did not intend to spite my brother when I beat him in the political debate.
The sisters played against each other in tennis, But they did it without spite.

The sentence "The runner completed several yard victory laps to spite his opponents." uses the word spite as a noun.