“Handheld game console” in Japanese
Short answer
Handheld game console in Japanese is “携帯ゲーム機” (keitaigeemuki). Full meaning: handheld game console, portable game console.
Other ways to say “Handheld game console” in Japanese
携帯型ゲーム
keitaigatageemu handheld game console, portable game console; game software for a handheld game console
携帯型ゲーム機
keitaigatageemuki handheld game console, portable game console
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