That grid would need a really large diameter and length HVDC line. The cabling cost alone would be a fortune.
2008 electricity global usage total: 143.851 TWh. It has probably gone up since then but that is the number I could quickly find.
That means an average of 16 TW.
Half of that needs to be transported to the other side of the planet. 8 TW.
Let's assume the HVDC cable can handle 1 million volts, based on the Pacific DC intertie
That means a current of about 8 Mega amps is running through that cable.
Such currents require massive cables. Think big. Think 30 cm (a foot) across.
Since I don't have the time to do the proper estimations I'll assume it is 30 cm.
Volume of a 30 cm diameter cable around the equator is 19,793,200,000 m3
An m3 of copper weighs approximately 9000 kg.
That cable weighs approximately 0.178*10^15 kg. Single cable, we'll need 2, for a total of 0.356*10^15 kg.
Buying that amount of copper is bound to get you into trouble. You see, the problem is that the world yearly production currently is around 17*10^12 kg. You need 21 years of our current production to build your cable. And current copper production is not because it's fun. It's because we need that copper.
The network in the link you provided is even longer than that 40000 km.
And I haven't even touched insulating, supporting or laying the cable. That Pacific DC intertie is over land, with air as insulation. Air is cheap, but much of the grid will have to be across oceans. Water doesn't easily support the steel constructions to carry the cable. Nor does water insulate.
And there are the political issues. Not every country will allow laying your cable across their country for free.
Global grid seems interesting for the uninformed, but calculate for it and you quite quickly see why it isn't done yet.