I get what it is, but it’s completely arbitrary. No other meaningful stat is tracked from the beginning of the season. Nothing about goalscoring is enhanced by doing it early in the season as opposed to later.
It gets even more silly when players get disqualified if they miss the beginning of the season. Why would that be disqualifying for a personal performance metric? It’s totally arbitrary to say they’re disqualified because the first 50 games of the season hold more value. No, they don’t. Nobody thinks that is true on any topic other than trying to explain this stat.
The video game comparison doesn’t work here. The first 50 games of an NHL season aren’t the only ones that count. The whole season counts. Players and teams that can’t figure that out, usually don’t do so well in the springtime.
Just going to echo a few others here and say I'm really not sure I agree that arbitrary is the right choice of word here.
First of all, it seems to be a pretty universal phenomenon in sports that when the schedule length increases, a bunch of oldtimers try to make adjustments for the disadvantage faced by older players. The most famous example of this is the official asterisk that baseball put on Roger Maris' 61 home runs in 1961, because it took him more than the 154 games that Babe Ruth played in 1927. They made that distinction over a whopping 8 games, compare that to the NHL schedule length which has increased by more than 60% since 1944-45. It's not like a number was randomly plucked out of the air, 50 games was a full season back then. It's perfectly correct to argue that this is by now completely outdated and anachronistic in a league that has been scheduled to play 80+ games for over four decades now, in the same way that baseball eventually removed that asterisk, but in both cases that doesn't really make it arbitrary, per se.
Secondly, as already pointed out in this thread, I think you're somewhat overlooking the fact that many stats are expressed as the "fastest to X". Fastest to 1000 points, fastest to 500 goals, fastest to 250 wins, and so on. Chasing 50 in 50 is really another way of seeing how fast a player can get to 50 goals. And I think there's a bit more of a romance to it in particular because scoring 50 has become an iconic target round number that defines elite goal scorers more than any other statistical benchmark defines any other player type. Scoring your 58th or your 63rd or whatever to complete a stretch of 50-in-50 just doesn't have the same cachet.
As for your claim that no other meaningful stat is tracked from the start of a season, I think you're very much overestimating the importance placed on all split stats relative to seasonal stats. Every "single season" stat is tracked from the start of a season, and even among sophisticated observers like the participants on this forum those stats probably make up a significant majority of the inputs for player ratings.
I think there is a fundamental difference in the typical fan's imagination for year-to-date numbers than for midseason splits. Even in an age with access to exponentially more information, there are far fewer people going to NHL.com and choosing segments between specific dates than there are just looking up the current statistical leaderboards. Many players have had hot or cold streaks towards the middle or end of a year while largely escaping notice in the wider hockey world because it mostly blends into their overall season totals. My impression of awards voting for NHL history in the pre-Internet era is that the recipients were usually effectively determined well before the end of the season, because people had been checking the scoring charts on a regular basis for the entire season and that was reinforcing certain narratives about the players, and you pretty much had to pore over newspaper box scores with a calculator if you wanted to get any kind of split stats beyond the official tables. You can argue that this is something of a blind spot, that it is really an artifact of availability bias, that goals and wins count the same whether it is game 1 or game 82, and I'd say you wouldn't even be wrong. But again I'm not sure I'd call it arbitrary.
The last reason that I'm less comfortable handwaving this all away, on the History forum specifically, is that players have highly prized hitting that benchmark. I watched a bunch of Mike Bossy interviews, for example, and it's obvious that he really, really wanted to score 50 in 50. He considered that to be a notable achievement, so much so that I think it throws a lot of doubt on your narrative of the historical evolution of that standard.
Of course you could say that the players only cared because it got unreasonably and undeservingly hyped up, but you can say that about a lot of things that people value ("Why do a bunch of grown men and entire cities full of sports fans care about a silly silver cup?"). This has probably been reduced somewhat in the last 40 years, perhaps as the target seemed less attainable, but if lots of people view something as important than I think you have to at the very least interpret their behaviours accordingly.
I personally don't make any distinction between the first 50 games and any other 50 game stretch, Auston Matthews is on a historically significant goal scoring tear this year by any relevant standard. Yet at the same time, I think I can sort of understand the reasons why others might.