It was built for the Liberty City World's Fair and was not taken down, a reference to the Unisphere, which was built for the same reason.
Events of TBoGT
The Monoglobe makes an appearance in the The Ballad of Gay Tony campaign, at the end of the mission Departure Time. Gay Tony is waiting for Luis near the globe. During their conversation, Tony mentions that he used to play near the Monoglobe when he was young.
Events of GTA Chinatown Wars
In 2009, Huang Lee destroys the Monoglobe on orders from Lester Leroc in Grand Theft Auto: Chinatown Wars, with the intention of eliminating members of The Lost MC. The Monoglobe spun off of its stand and crashes into a nearby building, destroying it.