Bird brain-eating Mantis - how does it crack the skull?
The mantis doesn't need to crack the skull to eat the brain. It can get to the cranial cavity through an easier way: the eye socket.

Have a look at this image of the ruby throathed hummingbird (Archilochus colubris) skull:



Source: http://wildlife.ohiodnr.gov/species-and-habitats/species-guide-index/birds/ruby-throated-hummingbird

You can see the huge eye sockets. This image (not a real skull, but a plastic cast) shows that even more clearly (also Archilochus colubris):



Source: http://www.boneroom.com/uploads/4/8/1/1/48118243/s521972503441136676_p1061_i1_w640.jpeg

According to the original paper of the research, which was linked by the NY Times article and by your very question (Nyffeler, Maxwell and Remsen, 2017): 


  Bigas et al. (2006:237) described the feeding behavior of the mantids in the mist-nets:
  
  &ldquo;The modus operandi of the mantis seems to be to approach the bird,
  which is always hanging downwards, and then enter the cranial cavity
  via one of the eyes, feeding on the brain tissues.&rdquo; (emphasis mine)


If you look at the image you shared you can see that the mantis' mouthparts are positioned at the side of the hummingbird's head, which corroborates the claim that the mantis uses the eye socket to get to the brain tissue.  



Sources: 


Nyffeler, M., Maxwell, M. and Remsen, J. (2017). Bird Predation By Praying Mantises: A Global Perspective. The Wilson Journal of Ornithology, 129(2), pp.331-344.
Bigas, D., J. Piccardo, And J. L. Copete. 2006. Praying mantis killing passerines in mistnets. Dutch Birding 28:237–238.