The smart phone could be easier because you have less visual clutter to sort through or the line lengths are shorter. The Spritz also only shows one word at a time so there is no visual clutter at all. Your problem could just be the visual clutter. It creates a heavier processing load.

Keep in mind that Spritz changes more than one parameter. It displays only one word so there is no visual distraction caused by the previous or following word or words above or below. It puts that word at the prime spot in your vision so the letters are not viewed outside that position. It displays the word without context so the brain can only consider the spelling. And, yes, it creates a situation where the eye does not need to scan but that also reduces the processing load on the brain freeing up that processing bandwidth for deciphering the word.

So, your reason based on ocular motility is short sighted. Any of the other differences could contribute to the improved accuracy.