Learn Hardcore Hindi: रैकेट से शटलकॉक मारिए।

Because they are borrowed words. In modern Hindi, especially in sports, English terms are very commonly used instead of older Sanskrit- or Hindi-based alternatives.

So here:

रैकेट = racket
शटलकॉक = shuttlecock

They are simply being written in Devanagari, the script used for Hindi.

What does से mean here?

Here से means with, in the sense of by using something.

So रैकेट से means with the racket or using the racket.

This is a very common use of से in Hindi:

चाकू से काटिए = cut with a knife
कलम से लिखिए = write with a pen

Doesn’t मारना mean to kill? Why is it used here?

मारना can mean several related things, including to hit, to strike, and in some contexts to kill. The exact meaning depends on context.

In a sports sentence like this, मारना clearly means to hit/strike:

गेंद मारना = hit the ball
शटलकॉक मारना = hit the shuttlecock