Well, PCI-e 2.0 just supports double the bandwidth of PCI-e 1.1. A PCI-e 2.0 card will work in a PCI-e 1.1 slot, and vice versa (IIRC). It does not matter whether your graphic card has PCI-e 2.0 if you wish to upgrade the graphics of your computer, it is more important that your motherboard has such a slot.
In the specifications of your computer, it said that your motherboard was based on the AMD 780G chipset which provides a PCI-e 2.0 16x lane, and thus your motherboard has a PCI-e 2.0 16x lane. You can use a PCI-e 2.1 16x card if you would like to in a PCI-e 2.0 lane, however, I believe it is limited to PCI-e 2.0 features, although really PCI-e 2.1 doesn't seem to offer many new benefits at all.