However, the irregular tiles actually bother more than if it was a standard geodesic sphere which only had 12 pentagons. For one, the fact that tiles are different sizes looks kind of weird. More importantly, this tile layout could actually make an important strategic difference (much more than if there were only 12 pentagonal tiles). Assuming movement costs between adjacent cells are constant, a straight line may not be the fastest way between points anymore! Looking at the heavily distorted mesh example, I can see several places where a path through a few large cells has the same movement cost as the straightest path.
Also, a realistic simulation of global wind patterns isn't actually that hard. Since it's only long-term trends that matter (at least when it comes to shaping overall climate), it's not like you'd have to calculate detailed fluid mechanics models. A simple model of Hadley & Ferrel cells (which is key to having realistic deserts) would get you most of the way there. 
I enjoyed the entire article, but this was the main thing that stood out to me as well.
Fluid dynamics on a spheroid are extremely well documented, and incorporating them will help derive a lot of familiar features that are a necessary consequence of them. Trade winds, Hadley cells, predominant ocean currents (etc), these are all things that can be easily applied to the appropriate model.
Particularly when you look at precipitation, the reason we have massive bands of dry and wet areas is because we live on a giant spinning ball.
In any case, really interesting to read!
I would say there is nothing wrong with strategic differences, so long as they are irregularly distributed. Regular or predictable distribution would cause strategic ruts. Also, irregular movement costs are a feature. Ancient spice trading routes and deer paths in the woods rarely follow straight lines either.
I also think this could lead to a whole bunch of balancing issues that might not immediately be obvious. Although some random-but-fair differences in balance such as this are okay, they should be based on the terrain, resources, and other features that mirror the real world, not "this tile is just bigger".
There are always going to be points on a sphere that map poorly to 2D - if you've played Spore, think of the in-planet spaceship map, you wind up zooming through parts of the map and crawling through others while still going the same speed in-game.
So if you've got an east vector for every square that is a function of the location, that means there's an east vector field. Same goes for the other seven options. Might as well make a zero at the poles, since one zero is weird, zeroes that don't line up are weird, and no one wants to settle at the poles anyway.
I hadn't seen this approach before, but guessed someone would have thought of it so hunted down a discussion; The spiral I used is taken from here: https://groups.google.com/forum/#!msg/sci.math/CYMQX7HO1Cw/t... (see the rest of the thread, their motivation is minimising the potential energy of charged particles on the sphere).
And: "Climate Modeling with Spherical Geodesic Grids" from Sept/Oct 2002 - Computing in Science & Engineering