1. 50% of people do one or more searches on mobile. That's awesome from Google's POV!
2. The number of people who are using mobile for their Internet has exploded in only a few years, many of those people still use their desktop for search.
3. Many, many people still don't use their phone for anything other than texting and phone calls.
But here is the kicker:
4. Charles Arthur is extrapolating a measure of central tendency in a rather foolish way. He's taking the mean average of the number of searches from mobiles per day for an entire month, then he's extrapolating that none of those mobile users do any searches per day for an entire month.
In other words, he's saying that half of all users don't do ANY searches at all, whereas all that he can say is that on some days, some users don't do any Google searches on their mobile device.
And if that's all his statistics are showing, then I'm not exactly blown away with this insight.