Filesystem-sort my directory please
Bean, 116 121 118 bytes

Hexdump:

00000000 26 55 cd a0 62 80 40 a0 6f 53 d0 80 d3 d0 80 a0  &amp;UÍ b.@ oSÐ.ÓÐ. 
00000010 6f 20 80 0d 21 80 81 00 20 80 92 20 6f 53 d0 80  o ..!... .. oSÐ.
00000020 a0 78 20 80 83 40 a0 5d a0 5e 53 d0 80 d3 a0 62   x ..@ ] ^SÐ.Ó b
00000030 20 5d 20 80 8b 40 a0 5f a0 60 a0 65 a0 6e dd a0   ] ..@ _ ` e nÝ 
00000040 61 50 84 d3 a0 62 20 5e 20 65 4e ce a0 5f 80 4c  aP.Ó b ^ eNÎ _.L
00000050 a0 60 8c 20 61 80 53 d0 80 d3 50 80 a0 60 20 80   `. a.SÐ.ÓP. ` .
00000060 b9 20 80 b3 53 50 80 a0 61 20 80 b9 a8 dc c4 aa  ¹ .³SP. a .¹¨ÜÄª
00000070 a9 a8 dc e4 aa 29                                ©¨Üäª)
00000076


Equivalent JavaScript (140 bytes, ignoring added whitespace for formatting):

f=s=&gt;s.split(/(\D*)(\d*)/).concat(s),
_.sort(
  (a,b)=&gt;f(a).reduce(
    (c,d,i,r,e=f(b)[i])=&gt;
      c||d-e||d.toLowerCase().localeCompare(e.toLowerCase())
  )
)


Basically a golfed version of the example implementation given in the question.

Click here for the demo!