Of course this only shows that the packages are different. Do you really think they shrunk the package without shrinking any of the die inside?
Of course. If the CPU is only 19mm^2 then neither the original nor final package is anywhere close to that small.
Shrinking the die/migrating it to a new manufacturing processor has got to be a lot more expensive than just shrinking the package as better packaging and PCB assembly technology is available (cheaply, with low failure rates). But with the latter alone they capture most of the benefits.
Package size is dictated by either the size of the die on it or the number of BGA balls necessary to cover power and IOs. The only way they could make it smaller is if the die got smaller or if they needed fewer balls. They couldn't significantly change the functional pinout because they didn't eliminate any of the major interfaces, therefore the only way the ball count goes down is if the power requirements go down. That means a shrink.
You're missing one: the size and pitch of the BGA balls shrunk while the die stayed the same. There isn't a one to one relationship between the die size or the die's pads and the size and pitch of the balls or leads in the package.
I'll attempt an absolute size comparison. There are some better PCB screenshots of older Wiis here:
http://hackmii.com/2009/08/wii-hardware-a-history/
This demonstrates the first smaller package for the CPU, and also that the capacitor sizes are a poor reference. So I'll take Grall's suggestion and use USB instead. USB-A sockets a little over 12mm wide. I used the middle picture for the original dimensions since it's less distorted. In this shot the USB is just on the edge of the picture so I estimated it, it could be a little off. But this is what we get:
Original Wii USB: 100 pixels wide
Original Wii CPU: 172x158 pixels (21x19mm^2)
Original Wii GPU: 246x226 pixels (30x27mm^2)
2008 Wii USB: 92 pixels wide
2008 Wii CPU: 118x122 pixels (15x16mm^2)
2008 Wii GPU: 222x246 pixels (29x32mm^2)
Wii Mini USB: 27 pixels wide
Wii Mini CPU: 32x32 pixels, 14x14mm^2
Wii Mini GPU: 58x58 pixels, 26x26mm^2
According to reports, Wii's original CPU die (at 90nm) is 19mm^2 and the original GPU die is 70mm^2. That works out to about 4x5mm^2 and 8x9mm^2 respectively.
The die size for Wii could be wrong, but it fits well with the die size report for Gamecube, and more importantly fits with the die size for Wii U that can actually be measured. So assuming that these sizes are in fact correct we see that even the current packages are much larger and can still easily accommodate an original die without shrinks.