지켜보다 is watching and keeping watching — monitoring, keeping an eye on — rather than simply seeing something. The -게 slot gives the attitude behind the watching: 흥미롭게 (with interest), 흐뭇하게 (fondly), 엄중하게 (sternly), 관심 있게 (attentively). 지켜봐 주다 asks someone to keep watching kindly, which is what a broadcaster says to the audience.