Counterpoint: I don’t think aoe2.net or any 3rd party non-Microsoft entity should have access to player stats, game recordings, or chats that are in those recordings; let alone be able to disseminate that info across the globe via a lookup system – especially, but not exclusively, data related to single-player and private or unranked multiplayer games. And even if Microsoft had stats (which they do, because aoe2.net is probably using an API to leech the info) I don’t think they should have the right to post that info without express written consent acquired before each match.
There should be a pop-up before each match: “This match will be recorded for playback. Your private, personal chats will be displayed to the world, and the outcome of the game including APM and other stats will be indexed and accessible by random people of Earth, just like all the aforementioned stuff. You cool with that? Yes/No.” If you select “No,” then that stuff stays unrecorded and private; not accessible on aoe2.net or any current or future Microsoft website. How it’s legal to blanketly release all or a lot of this info (assuming they do, and I’m pretty sure they do) is peculiar