AX Spin system ordering
There are a few things that seem to be wrong with the diagram you present, but since your focus is on the relative energies of the $\alpha$ and $\beta$ spin states I'll address only this. If you check a reliable source such as Cavanagh et al.s NMR textbook [ref 1] it is explained that 


  the state with $m=+\frac{1}{2}$ is referred to as the $\alpha$ state, and the state with $m=-\frac{1}{2}$ is referred to as the $\beta$ state.  If $\gamma$ [the gyromagnetic ratio] is positive, then the $\alpha$ state has lower energy than the $\beta$ state.


Therefore for protons $\alpha$ is lower energy (since $\gamma&gt;0$). If the nucleus is $\ce{^{15}N}$ ($\gamma&lt;0$), $\beta$ becomes the lower energy state. 

So while your concern is valid, it is a relatively minor flaw (in my opinion) with the diagram. Good for you for noticing it.  

Reference


John Cavanagh, Nicholas Skelton, Wayne Fairbrother, Mark Rance, Arthur Palmer, III. Protein NMR Spectroscopy, Principles and Practice, 2nd Edition. Academic Press, 2006, ISBN: 9780121644918.