Well the video card is specified at 350W, so even just that is a stretch 
PSU claims are usually overstated, but that's a pretty significant disparity to risk...
I know you mentioned you were building a gaming rig, but you might be working against yourself by starting out with that mini case Acer PC. They're really designed to be small, definitely at the cost of upgradability. Even if you could find a way to cram the upgrades in to make it work for gaming, it's going to be wayyyyy more likely to overheat.
At the very least I imagine you need better than a 220W PSU anyway. It depends on what you're playing I guess, but I doubt there are many video cards that would run on 220W that could handle anything even moderately recent.
If you want to put it in this http://www.futureshop.ca/en-CA/product/acer-acer-a
I also checked a power supply calculator (estimator) on the web and it suggested that you would need a minimum of 250 watts. I would NEVER recommend going with the minimum wattage needed for a PSU (power supply unit). For a couple of reasons:
1 power supply manufacturers often overstate what thier PSU can actually do (as was mentioned above) 2: PSUs degrade over time (that is a power supply that CAN output 250W today may not be able to do this in 6 months
3: when running a PSU at max load constantly (or at least when gaming) will 'cause the PSU to wear out 4: when a PSU dies, it often takes all or some of the computer with it.
also, since you're wishing to go with an AMD APU i would suggest waiting to get a graphics card that can work in tandem with the on-chip graphics (this tech is called hybrid crossfire) you want to get the A6-3650, this chip works well with: the Radeon 6670 OR Radeon 6570 OR Radeon 6450. The higher the model number the better the performance.
a Mini-itx motherboard:
