なりそびれた comes from なりそびれる, meaning to miss the chance to become something or to fail to grow into a role. In the lyric, 「大人になんてなりそびれたままでいいの」 means “It’s fine to remain someone who never quite became an adult,” giving the word a playful, rebellious feeling about refusing to conform to adulthood.
King Gnu open this one with an admission: 「ダンスなんて上手く踊れないけれど」 (I can't really dance well) and 「イケてるステップなんて刻めないけれど」 (I can't pull off any cool steps). Then they shrug it off: 「誰も見ちゃいないし気にしないで」 (nobody's watching anyway, so don't worry about it). イケてる is casual slang for "cool" or "on point", the kind of word you'd hear from friends, not in a textbook.
The setting is very specific. It's 「夏の終わりの熱帯夜に二人」 (the two of us, on a tropical night at the end of summer). 熱帯夜 literally means "tropical night", a real Japanese weather term for a night when it never drops below 25°C. Everyone else is asleep, and the hook says so plainly: 「皆寝ちゃったよ 今夜 世界は僕らのもの」 (everyone's fallen asleep, tonight the world is ours). The world shrinks to two people, which is where the small world of the title comes in.
The chorus is the part I love most. 「大人になんてなりそびれたままでいいの」 (it's fine if I stay someone who missed the chance to grow up). なりそびれる means to miss your moment to become something, so it's less "I refuse to grow up" and more "I sort of didn't get round to it, and that's okay." It's followed by 「勝手に世界は回っても」 (even if the world keeps turning on its own). There's a sneaky little dare in the bridge too: 「息を潜めろ街が寝静まるまで」 (hold your breath until the town falls quiet), then 「恐れずにこの夜に飛び込むの」 (we dive into this night without fear). It reads like two people sneaking out, a bit giddy, slightly ridiculous, and completely happy about it.