It takes place in the Wind Waker timeline. In the demo there is a Korok NPC you can talk to and I believe it gives you an item.

Wonder which timeline Wild Link is from? Adult Link timeline is ruled out due to know chibi-fied Link, and Young Link timeline is ruled out because of no sign of OoT Hyrule or Twilight Realm Hyrule. I'd wager it's either the original timeline after Skyward Sword as there's no towns and just Hyrule Castle, which was the setting in Skyward Sword, and judging from the overgrowth of the Master Sword, it could be possible it's in the Link's defeat timeline as the Master Sword is located in LttP and LBW in the Lost Woods where overgrowth is apt to occur.

tl;dr: Breath of the Wild could either be in the original timeline or in Link's defeat timeline, as there's insufficient evidence for young or adult Link's victory timelines.