Given that the Indians could barely hit the ball Wednesday, striking out twelve times and not collecting their first base hit until the sixth inning, there's a pretty fair chance they were going to lose Game 2 no matter what quality of defense they played, but if they're going to recover from their worst performance of the postseason and pick up the three wins standing between them and the franchise's first World Series championship in 68 years, their defense is going to have to be a lot better than it was last night.
The third batter of the game, Anthony Rizzo lined a ball down the right-field line. Kris Bryant, who'd been on first base, never stopped running, and there should have been a close play at the plate. Instead of throwing to the cutoff man though, Lonnie Chisenhall made the strange decision to throw to second base, allowing Bryant to score the game's first run without any sort of play at the plate. We'll never know what would've happened if Lonnie had thrown to Jason Kipnis, but given that Bryant was only halfway between second and third when Chisenhall got to the ball, it seems likely that a good relay would have nailed him. (MLB has not made the video of that play embeddable, but you can view it here.)
In the top of the fifth, with one out, Rizzo on first, and the score 2-0, it was Ben Zobrist's turn to rip one down the line. This time, Chisenhall slipped and fell before he could field it. If he'd fielded it cleanly and Chicago had been as aggressive on the bases as they had been in the first, Rizzo would have been out easily.
It's possible that if Lonnie hadn't fallen, Rizzo would have been held at third, in which case there would have been two on and two out. Chicago may very well still have pushed Rizzo across the plate in that scenario; the next man up (Kyle Schwarber singled), but it's also possible that things would have played out in a way that didn't include runs scoring. And yes, a player falling down on what was almost certainly damp outfield grass is not egregious, but it's not as though players were falling left and right.
Three batters later, an easy grounder to Kipnis should have ended the inning, but Kipnis bobbled the ball twice, allowing the runner to reach base. Bryan Shaw then walked the next two batters, putting another run on the board. (Video of the play can be found here.)
Two innings later, in the seventh, Francisco Lindor made a tremendous diving stop on a ball hit to his left. His toss from the ground to Kipnis was a little high, but an easy play to make; Kipnis didn't make it though, and was charged with his second error of the game. The Indians managed to get out of that inning without any runs scoring, so it didn't change the score, but it was still a significant blunder.
Only one of Chicago's five runs came in an inning that was free of any defensive misplays by the Indians. Odds are one or two of those other runs would have scored anyway, and the difference between a 5-1 loss and a 3-1 loss is non-existent as far as history as concerned. There's a non-zero chance that none of those four other runs would have scored though, and it might have been a 1-1 game. There's also a non-zero chance later events would have played out differently, and the Indians, with different batter/hitter matchups and decisions, would have scored a second run.
Whether the ultimate outcome of Game 2 would have been any different or not, the outcome of Games 3, 4, 5, and maybe 6 and 7 could certainly be affected by plays like the ones the Tribe made last night. The Cubs are plenty good enough to win without being handed extra opportunities, so the Indians need to tighten up their defense between now and Friday night.