So what makes this show compelling is unclear.
One aspect that dearly works is the lead. Unlike Linda Hamilton who in T1 and T2 were the movie’s weakest link, in this show Sarah Connor is played with restraint. There is none of the mayhem or chaos or bad acting. Instead we have despair, desperation and hope finely balanced.
Another aspect is the terminator who acts as John’s bodyguard. Both in T1 and T2 the future warrior was poorly acted. In T1 the actor delivered some memorably poorly acted lines. In T2 Arnie had become such a star that we had him attempt to show the softer kinder gentler Terminator. So much so that he obliterated some of the scariness of the machines.
In this show the terminator is disturbing. We don’t see her as a loveable Data, the robot from StarTrek like we did Amie in T2, but something sinister. Something that could blow up at any moment in time. And that makes you uncomfortable. She’s almost like a pet lion. Sure the lion seems friendly, but is it, really?
So maybe it is the acting and the character development.
But that discounts the plot a lot. One of the frustrating aspects of the movies was the fact only one person got through. But with a time machine I could keep trying again and again. One angle the series has explored is the notions of a temporal war. Essentially both future factions send commando’s into the past to perform missions to ensure final victory. In come cases John stumbles on these plots must deal with them.
Again after 4 episodes, I must strongly recommend this show.