While it's true they have transformed into a very good team, if I had to guess, they won't win the league with Klopp.
As their attacking game relies so heavily on attacking transitions, it's difficult to see this style of play being maintained consistently over the 38 game season. To me, this is because Liverpool rely a lot on how the other team sets up against them - there is clear daylight in their performances against City this season vs. the games against us. Pep being Pep was inclined to play close to his regular system, being brave on the ball, trying to play on the front foot, etc cetera.
Look at the 3-0 against City in the CL. All 3 goals came directly from the next attack after they won the ball from City on the floor. I would argue that Liverpool are the best side in the world at attacking transitions, and so trying to play this style of play against them is inevitably going to be extremely dangerous and difficult. The difference in the Premier League is (especially smaller) sides are far more reluctant to give Liverpool this chance. Sides like Burnley and West Brom, who don't have the technical ability to consistently play out from the back, have no option but to find alternative ways of starting attacks, ie. 'going long'. For me this is a good tactic against Liverpool because it means there is less chance of defenders being caught out of position and punished. Of course if you are actively trying to play out from the back your fullbacks, deep midfielders etc. are going to move out of their starting defensive position to aid the build up. Naturally this is exactly what the likes of Salah and Mané want as it gives them space to attack.
Conversely look at how Young, Matic and Sanchez helped to crowd out Salah in the win at OT. Young only ventured forward at safe times and so there was so little opportunity for him to play his game and get at us. Over a 38 game season I don't think Liverpool are suited for this type of match, which will inevitably happen as it is the 'obvious' way to play against them. Because Liverpool are so much better when the opposition play into their hands, I don't think their CL standards are maintainable over the course of a year. Inevitably you then must look at the other factors coming into play like fatigue and injuries.
Of course this could prove to be complete tripe and they walk the league next season. It's not intended as a criticism of them or Klopp, just an observation and prediction from myself.