I think that what you want is called a picocell or femtocell. It acts as a tiny cell tower. I don't know if they are available for GSM networks. I expect so since AT&T uses GSM and one of the ways they mitigated their spotty coverage was to sell people a picocell.
The opposite is a 'gateway' which connects a land-line telephone to the GSM network as if it were a mobile phone.
The GSM/GPRS modules like the one in the video lets your Arduino act as a cellphone. It was making a call through the GSM network to the phone and sending an SMS through the GSM network to the phone. Both the module and the phone required active GSM accounts.