Error #1: despite Google explicitly stating half the searches are mobile and "this excludes tablets" [1], the author accidentally included Android tablet users in his calculations (he used the "1.4 billion" Android users figure). At least 200 million of these 1.4 billion are Android tablets, so the number of Android phones is 1.2 billion. This sets the mobile searches per device per day at 1.04.
Error #2: the author's gross rounding of the number of PCs in use is incorrect. It was already estimated at 1.5 billion in 2013, and said to grow to about 2.3 billion by 2015 [2]. Just plugging this number into the author's math, and this sets the desktop searches per device per day at 0.87.
So fixing these two errors alone and you end up with the conclusion that mobile users search a lot more than desktop users (1.04 vs. 0.87).
[1] http://blogs.wsj.com/digits/2015/10/08/google-says-mobile-se...
[2] https://www.gartner.com/doc/1602818/forecast-pc-installed-ba... (That's the most current estimate I could find —honestly 2.3 billion is likely an overestimate because they didn't forecast the tablet growth, but if it is anywhere above 1.85 billion my point and math stands).