Indians Tigers Balk

He started then stopped.  The pitcher has to make one continuous motion when going from the stretch to the set position.  He can make adjustments before he starts, but once he starts to come to a set me must do so in one continuous motion,  Then he must come to a complete stop with both hands in front of his body. 

He started his motion and stopped.  It was a clear balk that was immediately called by two umpires, recognized by several players and argued by no one.  Unfortunate and bizarre for a game like that to end that way but no question about the call.

Then according to that rule, if the pitcher were to make a circle motion to signal he wants to go through the signs again, would that also be a balk? I know its a bit of a stretch, but could there be an argument that the pitcher was doing just that?

That would be one of the preliminary adjustments I was referring to,  Other examples would be adjusting his cap, tugging on his clothing, digging with his spikes, even wiping sweat from his brow (must give a wipe on his clothing after on that one.)  The umpires must be certain that he has clearly started his motion towards the set position.

No doubt that it was a balk. Here's why he balked...With a runner on second base, the catcher/pitcher must have a series of signs they go through before each pitch. Either Albuquerque forgot or the series of signs that Avila was going to go through - the first sign was the "live sign". If you look closely, Avila gives him "pinkie away" or Fastball Away. Then, Albuquerque flinches because that's the pitch he wants - fastball away. Avila begins to give another sign, but the balk has already occurred. GAME OVER!

The umpire must judge what the pitcher was doing.  In this play, it was obvious.

Note that the other items you mentioned would, by rule, have been balks in HS ball until recently (last year?  this year? -- I forget).