Unless the NHL decides that finishing the 2019-20 season with an abridged playoff format is more important than having close to a full 2020-21 season, I don't see how another game is played.
I don't expect larger scale crowd gatherings (100 people) to be permitted before July. The focus is currently on flattening the curve. Until we're on the decline on the other side, restrictions on large scale events will hold. Which means we need to reach the peak and ride it out, plus see a significant decline in new and existing cases - which can't be quantified accurately, so they need to play it safe or risk a second/third wave outbreak.
Even if you take out the attending crowd an NHL game needs: 3 officials, 38 players, an emergency backup goalie, 2 coaches, 2 assistant coaches, 2 team medics, 2 equipment guys, 2 team doctors, 4-6 play by play guys, 2-4 for the camera crew and 2 rink staff (Zamboni driver, plus a helper in case the glass needs repairs). That's 60 staff/players at an absolute barebone minimum.
I'd go as far as saying that you likely have more than one team medic (at least an additional athletic therapist or 2 per team), team equipment guy and 2 rink staff. That's no ice crew to scrape the ice during tv breaks. No security in the building. I'd be surprised if a low staffed event had under 75 people in the arena when attempting to minimize the number of people working.
At what point does the government allow gatherings for 75+ people on a regular basis? Additionally, you're going to be gathering players and staff from all across North America - which means flying across borders which isn't currently permitted without a self isolation period...
Realistically, you'd be gathering all the teams in one place, doing a quarantine for 2 weeks and then giving them a training camp for a week, plus playing the playoff format. What city has NHL size ice and is isolated enough to make players and staff from 16-20 teams (approx 30 staff per org, without extra - we're talking accommodations for over 600 people) feel safe gathering in the current times?
I think we're months out from seeing small gatherings of 10-25 people being permitted. I don't foresee hockey happening before September (with all teams needing a training camp to get back up to speed), at which point the league is better off proceeding with the 2020-21 season than holding playoffs delaying the next season by at least 2 weeks to hold a single elimination 20 team format (5 rounds, including the final with a bye for division leaders to the 3rd round). Any kind of proper series delays the next season by months instead of weeks.
I think the league will desperately look for a way to not write off the 100+ games of the 2019-20 regular season and playoffs revenue, but I don't foresee them finding a way to do so if restrictions on travel and gatherings aren't beginning to lift before May or June.