Thanks for the clarification on terminology - I too was wondering what the "rug" was.
Thank you also for the closeup, and the proposal that there is more going on here than a single plant.
Instances like this shrub mass - in a public setting where it is likely managed meagerly by non-horticulturists - often results in seedling species growing among the original plants, but getting sheared into a common shape along with the primary species.
The nearest vigorous stems in your last image appear to me to be an Elm seedling of some sort. It has a dentate (toothed) margin on alternately arranged simple leaves. If further zooming was possible, you'd likely note an oblique leaf base on them.
The rest of the majority shrub mass (background) appears to be opposite in leaf arrangement. Since there is no clarity to leaf morphology, buds, and stems - I will only hazard a list of commonly used ornamental plants that are likely used in Des Moines that fit that characteristic.
Forsythia x intermedia, Weigela florida, Euonymus alatus, Hydrangea paniculata, and Lonicera sp. are all utilitarian species that one might see in a location like this.