TOKYO—If Nintendo Co. finds success with its videogame console, Switch, it could brighten the future not only of Nintendo but also of Japan Display Inc., a struggling display maker that won the contract to make the Switch’s screens.

People familiar with the matter said Nintendo picked Japan Display as the exclusive supplier of the Switch’s 6.2-inch touch-sensitive liquid-crystal display. The Switch, which can be used both as a stationary console and a hand-held player on the go, is to go on sale globally March 3.

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