What is the geochemical origin of carbon dioxide with the 'white smokers' of the Champagne Vent?
Observations and geochemical measurements presented in a study published soon after the article in the question, Submarine venting of liquid carbon dioxide on a Mariana Arc volcano (Lupton et al. 2006) sheds considerable light on the processes involved in the unique Champagne vent.

The key unique features of the Champagne Vent are the presence of CO2 droplets and the CO2 concentration - 2.7 moles/kg - the highest for any underwater hydrothermal vent. This concentration is also supersaturated, being considerably higher than what should be possible at the temperature and pressure present at the vent.

The proposed model, based on Lupton et al's observations and measurements, suggests that there is a subsurface layer of CO2 liquid and hydrates that is penetrated by the vent, resulting in the CO2 becoming entrained in the hydrothermal fluids, providing for the observed 'cold' CO2 droplets and also increasing the concentration to supersaturation levels.

Lupton et al. also explain that from geochemical analyses, the source of the carbon is mostly (90%) from subducted carbonate melt, with a small amount coming organic matter and mantle derived carbon.  Further, chemical measurements reported in the later research Chemistry of hydrothermal plumes above submarine volcanoes of the Mariana Arc (Resing et al. 2009) indicate that there is an absence of chemical reactions between the host rocks and the CO2 and further suggest that the magma chamber is deep within the NW Eifuku volcano (Champagne Vent source) and the gases rise into colder, older substrate.