Just what exactly do you think genetically-modified organisms are and are used for?
Invasive species are a secondary issue that occurs regardless of genetic-modification. In fact, introducing selective genetic markers into a GMO crop can prevent it from becoming invasive due to nutrient requirements. Every one of the invasive species on that list became invasive without any pre-existing modification, and virtually none of them were intentionally introduced either (as crops are).
Most GMO applications are relatively benign and are used only in plants - encouraging disease resistance, overall hardiness, longer growth season, larger growth, higher productivity. In fact, while all crops today can be considered genetically-modified, very few are actually subject to true molecular genetic manipulation. Most are simply cross-breeds of artificially selected individuals which produce strains.