You are not reading it correctly, but this is due to a misunderstanding of the information in how it will interact with in game attributes. It will not significantly increase snowballing to the extent that all of the doomsayers are bemoaning on the forums.
The change is a small percentage increase to the amount of damage that minions do to minions, 5%, that increases by level advantage and turrets down in the lane. What isn't being accounted for is that minions don't do a lot of damage. A Melee Minion only has an AD of 12 and it goes up by only a half point, 0.5, every three waves. So that kinda means that if a game goes on long enough for a Melee Minion to get an AD of 30, which is going to be well over 50 minutes, an advantage increase of 15% from both the inner and outer towers being down and no towers taken in that lane, that would mean that the minion has an AD of 34 instead of 30. That's... not a lot.
The problem is more that it changes how waves will behave and they won't really behave as predictably as before.
What would be interesting is seeing how it would play out, it's not as simple as "the team that is ahead is more ahead". It means that the minions of the team that is ahead will be pushing a little more. In terms of ending games sooner, it should function that way in that an undefended turret would have minions near or on it so that the team that is ahead can rotate and take it. However, if the behind team does defend it, they will have minions pushing near their tower allowing them to farm up and gain gold and experience without the risk of overextending to farm and getting picked off.
Interestingly, it may also mean that as minion waves won't freeze at some point in the lane and growing in size, we won't be getting those huge waves that can take a tower alone anymore.
Should leaverbuster maybe be a bit more aggressive in punishing the DCs if we're looking at an option above?
No, that won't solve it. Having Leaverbuster being more aggressive will not change any of the conditions that cause players to disconnect from or never connect to the server. A better solution would be to simply just not have games start with only 9 players.