A monopoly should be defined by barriers to entry, not just market share. There's nothing preventing other large companies from entering the search space, and in fact many of them have (yahoo, microsoft, etc). There are true monopolistic firms like Comcast or Time Warner, where there are serious logistic/economic barriers preventing other firms from entering the market. This doesn't seem like one of them to me.
In the US "natural" monopolies are allowed to exist, the best example of this being Microsoft with their Windows operating system. What isn't permissible, is using that monopoly to advantage your other products, and possibly more importantly disadvantage products of your competitors.
Could you explain how an operating system is a natural monopoly?
Development of a new OS isn't cheap, but isn't prohibitively expensive either. It also isn't undesirable AFAICT.