What would define "standard" in this case? When the majority (over half) have at least a 1920 x 1080 resolution or greater?
On what platforms? PC? Gaming console/TVs?
Personal anecdote replies on a tech enthusiast forum will not get you the answer you need. You need to look at the actual data. I would say this likely happened in the 2010s, not 2000s. There's not a chance it happened that early. The early and mid 2000s were predominantly CRTs and the early 5:4 (1280 x 1024) LCDs. The 16:10 widescreen LCDs came around in the mid to late 2000s, and then they shifted to 16:9 and mimicked the TV market. This all started happening in the 2000s... but the majority probably wasn't on 1920 x 1080 or greater until well until the 2010s. I would imagine 720p and 1366 x 768 remained the most common resolution for far longer than most people would think. Want to know when quad cores finally overtook dual cores on the Steam hardware survey? Mid to late 2010s. I bet that's later than most people would have imagined. And that was gamers; regular users would have kept them around as the majority for even longer.
It's also hard to define what a "gamer" is because as far as I know, the only two types of readily available data you could look at for something like this would be the ones that analyze internet users' resolution/OS/etc, or the Steam hardware survey data. Both data points need taken with "a grain of salt". The latter would sound better to use for gamers, but how many people "play games" but don't play on Steam? Are those casual or other platform gamers not gamers? I wouldn't say so. What I'm saying is looking at Steam's data would probably be fine as a compromise, but you'd have to accept it might be a bit ahead of the real average unless you're specifically looking at gamers on Steam. Including other PC gamers or console gamers makes this... nearly impossible?
So the question you're asking is incredibly tough to answer, but if I were trying to guesstimate this, here's what I'd do.
Look back on the internet archive for the Steam hardware survey results.
Look at when it was that "1080p or greater" became the resolution that the majority (50%+) were on. A very important distinction here is that you'd have to do some manual work here because it might list 1080p as the single most common resolution starting at a certain point, but if it was the single most common resolution out of dozens and dozens, but had less than half of the people at or above it, I'd say that's not "standard", at least if you're not defining standard as the defacto majority.
I'm too lazy to do that myself right now, but I'm going to hazard a guess "sometime in the 2010s". When, exactly, I don't know. Mid 2010s maybe? Even early 2010s would surprise me a bit.
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