It's not entry that failed them but their adamant decisions towards mobile platform did lead to failure.
Xiaomi arrived super late in the android market. But compared to Oppo, Lava, Micromax brands, they are selling products lot quicker. So it's not about late entry but the wrong decisions. Xiaomi made android look simple, cute and quicker with minor changes and improvements. And they kept cost low as well.
Some of the wrong decisions for Microsoft include - Metro UI. Forcing UI which is harder for people to understand lead to lack of buyers. They even failed with Windows 8 for that matter. And that's why they got back into Windows 10 with responsive look instead of metro UI.
Another bad decision they did is removing symbian. What works to make money should not be disturbed. They did that with nokia and losses began coming into it.
Now if they want to survive in Mobile space, they have to think of super easy interface for people. And cost that justifies the purchase. This is one reason any company that gets into android market is making money. UI remains simple and they just have to compete on specifications and quality of specs. Microsoft is still in 80s and 90s attitude where they want name to sell instead of features or the customer demands.