For some reason its possible to teleport throw end gateway (appears after killing dragon) while riding entity by simply going into portal block. Seams to work with any entity. Issue is that after teleportation player will be glitched out as entity dint teleported properly with him, reloging resolves issue. And just to add, in case you teleport throw end gateway with ender eye then teleport cause will be correct as END_GATEWAY, while teleportation with entity without throwing ender eye will result into UNKNOWN. 

To top that one up. If you are riding and trying to teleport throw end gateway with ender eye, it will not teleport you and sometimes will glitch out and will send you to the destination, which seams to only be client sided as you cant interact and reloging will return you back to previous position.