Xbox One has released the ability to emulate a wide range of Xbox 360 games.
Does the Xbox One retain the ability to use the 3D display feature of select Xbox 360 games?
Yes, but it's contingent on more that just what, how, and a basic whether Microsoft decides to implement it between consoles.
"3D" games are something that never really "took" for a number of reasons and the titles produced with 3D capabilities are very small and shrinking, especially given the struggle to keep high frame rate on resolutions at and higher than 1080p (and with HDR, which are contingent upon those wonky HDCP 2.2 requirements and quality and bandwidth of HDMI cables); there are a lot of technical bottlenecks mixed in with nearly non-existent consumer demand.
From this post on ExtemeTech, its stated that:
Of course, stereoscopic 3D gaming remains possible on both the Xbox One and PS4, but neither company seems interested in pursuing that angle. Considering that many Xbox One games struggle to hit decent frame rates at 1080p without 3D support, rendering two different perspectives at once would only make matters worse.
Without delving too much into the technical side of the above (this discussion on format of UHD and 3D can explain why it's not a priority for the industry to have 3D on BluRay at 4K / UHD along with how it's accomplished and thus not really an advance but a layer to ease a transition away from the technology), the XBOX One does is not natively backwards compatible - rather unlike earlier console generations with backwards compatibility, there is no secondary hardware chip that processes the old original format disc on the fly, as is. In this case, the XBOX One emulates the XBOX 360 just as the PlayStation 3 emulated earlier iterations of itself to be backwards compatible.
Games that were 3D compatible are still capable of being reproduced in 3D. However, the 3D output on games from the 360 to XBOX One is dependent upon the resource requirement and if the emulation layer detects a 3D capable TV and if the TV uses that layer because a growing number of components are geared toward future technology and pushing HDCP rather than 3D.