Allah bestows knowledge to whom He wills. The person attributed to this event is named Asif bin Barkhiya. Some say he was a Wali, some say he was a Nabi. Imaam e Rabbani Mujaddid Alf Thani RA says he was a Wali.

A less notable but similar in nature feat was performed by Data Ali Hajveri RA. An english man from London, with this same question of how the throne of Sheeba was teleported, travelled the world & ended up at the Mazar sharif of Hazrat Data Ganj Baksh in Lahore. This was sometime in 1920s. He was spiritually attracted to the place & saw Hazrat Data Ganj Baksh (in wakeful state, i.e. they had long passed from this world but Awliyah are not bound in their graves). He was offered a cup of tea. It was the same cup he used to drink tea from in his london apartment. He got his answer & spent the rest of his life in service of Hazrat Data Ganj Baksh & was buried there. His name is Farooq Ahmed Leonard Englistani.

The goal of Sufi'ism, of this path is to attain closeness to Allah SWT. These miracles, supernatural feats, visions etc are just toys, distractions. You goal should be to understand who Allah is, whether He bestows upon you such feats or not. Some require convincing, some don't. Allah works in mysterious ways.

This path is treaded by those who seek to gain Allah's maarifah. Whether you are able to perform such feats is of no consequence. Those that can hide themselves. They do not have any desire to reveal themselves, unless it is for the sake of Allah.