I think its more that originally GPU compute proved that deep nets are possible to train and give good results which lead to more research on them and the development of things like ReLU and ResNets.
You're right. It is partly greater computing resources, partly recent algorithmic advances, and partly the availability of large amounts of data which the more complex networks require.
Of course GPU-based training has helped a lot, but my impression is that these theoretical breakthroughs were also important.