You are confusing the voltage ratings verses the power handling requirements. First, you need to look at the a/c unit and see what voltage it runs at (120/240 are the two likely choices). Then, look at the existing plug. It could be a 110vac 15A, or 110vac 20A plug, or it could be a 240vac plug that each have the pins in a different configurations. The unit will say something about how many watts it draws, and likely will also list how many amps.
Once you know the power requirements of the a/c unit, THEN you can match it up with an appropriate cord. The 300/600 v thing is how well the insulation can protect from arcing through the insulation to something, maybe you, maybe an adjacent wire. The rating needed depends on the voltage you have at the wall plug. The wire you have is capable of powering the a/c unit in all likelyhood, but doesn't meet the code requirements for an appliance power cord. Now, we could be wrong...I'm not familiar with all of the designations on that wire you have. 10g is plenty large for any window a/c unit I know of, but it may not have a proper outside insulation that meets the abrasion, flexibility, etc. requirements for a power cord; it is probably rated for use in a wall or protected some other way. Attaching 10g wire to a power plug, or even the a/c unit itself may be a pain if there are screw lugs...if it was designed for say 12g (which is smaller - in wire gauge, lower numbers are bigger wire conductors, and once it gets to zero, they start adding more zeros so 00 is thicker than 0).