If someone proposes a method as an alternative for a field, they need to test this method on the accepted benchmark dataset for that field. For object recognition in static images this dataset is the ImageNet competition. Computing power can be bought from AWS if no cluster is available. The lack of it can't be an argument.
Not saying that the paper has no reason to exist, I think it is generally well written and decision trees certainly deserve attention. If they can do representation learning on high level this is certainly something to look into. But it shouldn't claim to be an alternative to state-of-the-art deep learning if there is no data for this comparison. Everyone can solve MNIST (or even CIFAR).