I think Intel's approach to competing with the likes of ARM and other "mobile" processor manufacturers is to capitalise on the backend enterprise market. Intel know that if there are x new phones (with third party mobile processors) sold, then phone manufacturers and service providers are going to need to purchase y new server processors (high end Xeons = high margins). This is more or less what has kept them alive within the industry and it should continue at least in to the medium-term.

Many of Intel's products, like their modems, have just been ploys to sell more desktops (i.e. sell more desktop processors). They've found that the mobile processor industry is just a race to the bottom so they're sticking to the high-margin desktop and server processor sectors.