Maybe I'm cynical but this strikes me as bogus. In the case of low pressure gas why not just use air onsite? Both flue gas and air are mainly nitrogen. On the other hand liquid C02 requires tremendous energy to scrub and compress. A food processing plant near home uses it to make beer flavouring extract worth $$thousands per ton. Since neither the US nor Canada have carbon taxes there must more reasons than EOR to use up perhaps 40% of the surface plant's power output. Could it be there is a government handout to 'prove' it works? You also need to factor in the extra CO2 when the EOR is eventually burned.
The reason for using CO2 os probably its low critical pressure (ie, relatively easy to "liquefy"). Lots of gases will probably do but CO2 is the easiest to work with for supercritical extraction.
Liquid CO2 has solvent properties that N2 and oxygen do not have.  For example, liquid CO2 is used in industry to extract caffein from coffee beans.  This is the so-called "natural" process of decaffination.

Actually, it is not exactly correct to classify the CO2 used in petroleum wells as "liquid".  It would be more correct to call it a supercritical fluid.