If you had this many you'd need a significant amount of ram, bear in mind if each of these calls php, and you're using fpm (recommended, don't use mod_php) you'll need enough ram for the php context/interpreter for each of these concurrent requests.
This very soon becomes many gigabytes...
I tried to come up with a "worst-case" scenario. Though, i might overestimate this number. (Again, no experience. Never released a commercial game so i can't even roughly estimate how many active players there would be.)
Question: There are for sure mobile and PC games which host their own leaderboards/stats on seperate servers. Are all of them always using dedicated machines or is there a scenario where a v-server (or virtual webserver) would suffice?
Note that "3000 concurrently active users" doesn't mean "3000 concurrently active web requests." A user will typically make a web request, it gets served pretty quickly, and then it takes a while before the next request is made. For example, if web requests are only made to update or read leaderboards, you can easily get maybe 5 concurrent requests when you have 5000 concurrent users (depending on game session length etc.)
If you are on a public platform, such as Google Play, iTunes Game Center, SteamWorks, Xbox Live, and so on, then leaderboards come with the platform, and you don't need to do anything yourself. If you're not on one of these platforms, then you need to either use a pre-existing game platform (Gamedonia etc) or roll your own.
