Neural networks already see in "higher dimensions" (whatever that means). Anyone who's ever used neural networks already knows each neuron's branch (i.e. dendrite) of an N-sized vector can already be though of as a "dimension" of a data set. CNN (convolutions) flatten that data (reduce it or seeing the same pattern over less "dendrites", much like PCA, etc.).
CNNs only make sense when working with image data anyways.
Not true, N-dimensional convnets, 1-d convnets (for NLP and time series analysis), spatially sparse convnets, graph and non-Euclidean space convnets, ... exist and are used.
CNNs are akin to multiscale wavelet transforms. They can be applied on different spaces (just as graph wavelet transforms exist).
Not true, CNNs are used for audio and text as well.
I don't think the title is clickbait, you may be misinterpreting it. Its referring to using CNNs on higher dimensional inputs, not that the layer has multiple dimensions (which has been done since the creation of convnets)