I'm still playing all EPs and a boatload of mods (heavy ones like NRaas StoryProgression) on a mid-range 2011 desktop. It's getting cranky on me mechanically here and there, but it's strong enough to run the entire thing. It's not the age of the system that matters here, it's the strength of the system components and what they are designed for. The HP model just mentioned falls short of what is required to run the game properly as it's just not designed for that kind of usage as @puzzlezaddict explains.
As a more extreme example, anyone can go online or into a discount department or office supply store and purchase a $250 (USD) modern laptop running Win 10. It won't play TS3 and isn't meant to. This one is a higher class than that and I'm sure it's great for what it designed to do, but still not high enough for TS3 or at least not the entire game at medium to high graphics settings. While price is not really the determining factor, and some laptops are more expensive because of how lightweight they are, this is why we keep saying that laptops that can run the entire game start at $900 or so.