Gilbert Cell Output Current
Is the load connected between the points 1 an 2? 


Something must be connected to points 1 and 2 that will provide enough operating voltage, and allow \$i_O\$ to be calculated from \$i_{O1}\$ and \$i_{O2}\$.


  Or is there VCC? 


It is the obligation of the circuit designer using the Gilbert cell to provide this.


  Moreover, if the load is connected between them, why is the current flowing on it equal to the difference of Io1 and Io2?


That depends on the load provided by the circuit designer.  It is the obligation of the circuit designer to provide circuitry that calculates \$i_O\$ from \$i_{O1}\$ and \$i_{O2}\$.

Check the documentation for the NE612 to see how it's done in an RF circuit (note that the NE612 has circuitry to generate the \$i_{X1}\$ and  \$i_{X2}\$ from a single external pin).

Analog Devices also sells a number of analog multipliers that are based on the Gilbert cell.