Where are they getting an additional 80+ players? Same place they get everyone else. AHL, Euro leagues, college, juniors, the standard mix.
As to watering down the league, I don't think much of that as an argument. Oh no, the median 4th liner is going to be slightly more along the lines of Anthony Richard than Garnet Hathaway, however will the NHL survive. On average, assuming the league expands by 4 teams, each of the existing 32 will have 1-2 players who would have been on their AHL 1st line/pairing instead of their NHL 4th line/3rd pairing. In the meantime, you may find a handful of players who turn out to be better players than you previously knew, like Marchessault and Karlsson in Vegas, because of the added opportunity that comes with the extra ice time. Then, over the next few years, the talent level resettles, as more players filter through the system, and it becomes a negligible issue again.
There'll be a few more teams at the top of the pyramid drawing talent up to that top level, and the rosters further down the chain will bring in people from that next tier, and so on until you open up more opportunity at the bottom for people who might not have gotten a break before. Ultimately, it just doesn't change things all that much IMO.