全部都错了，我完全没看懂。

也许themselves可以省去。

indulged

Those who indulge themselves with the Internet should cast their eye over the friendship and kinship in real life.

把in换成with, 把eyesight改成eye, 把to改成over.

People who overindulge in internet activities                  [1]
  should get more involved with friends and loves ones
           ^
    OR   find time to be with .... more often

  cast = 抛
  cast a line = 钓鱼投线
    NOT cast eyesight to
    BUT cast an eye towards __ = 朝 __ 快描一眼          [2]

[1] indulge occasionally = OK
     overindulge to the point of near addiction = not OK

[2] set one's sights on ... // keep an eye on ...   <- NOT enough correction，

those who indulge themselves in the Internet should cast sight onto the friendship and kinship in real life