‘Favourite, motive, get’ aren’t precise here. Most people are drawn to extreme sports by the adrenaline rush. The release of adrenaline is the main reason that people /engage in/practice/do/ extreme sports.

They are both grammatically correct but neither makes much sense. Infinitives and present participles can both function as nouns. Anywhere where "to get" is used as a noun, it can always be replaced with "getting" to produce an equally grammatical sentence, and vice versa. However, the meaning can change when you do such a switch.

Seeking adrenaline sounds best to me (I'm a native speaker) but getting some adrenaline sounds ok. (To get) some adrenaline doesn't sound natural (but you would be understood).