What does *players* mean in the context?

Clay just nodded, seeming rather uncomfortable about something. “Yes, so keep your hands off! She doesn’t need players like you chasing her around,” he growled with a threatening tone to his voice.

Does it mean something like a womanizer? Because the phrase football player is senselessly in the context.

"Player" here is a slang term for a certain type of womanizer. One hates to turn to Urban Dictionary as a source, but I'm rather fond of the top entry there:

A male who is skilled at manipulating ("playing") others, and especially at seducing women by pretending to care about them, when in reality they are only interested in sex. Possibly derived from the phrases "play him for a fool", or "play him like a violin". The term was popularized by hip-hop culture, but was commonly recognized among urban American blacks by the 1970s.

A certain class of low-rent, slack-jawed fuckups has decided that backstabbing and misogyny are totally radical, so the word is sometimes used as a compliment or term of endearment between male friends, as in the greeting "what's up, player?".

Agressively attempting to seek women is known as 'playing the field', as a sport analogy. Therefore, someone doing that is a 'player', and not a good match for someone looking for a more long term match.