すったもんだ is a vivid, colloquial Japanese expression for a chaotic series of arguments, complications, and ups and downs. In the song, it follows “winning and losing” and “breaking apart and coming together,” capturing the endless turmoil of everyday life in Tokyo.
King Gnu turn Tokyo into a ride you can't get off. The song opens with someone jumping onto the Yamanote, Tokyo's big loop train line, and going round and round until their head spins: "ぐるぐる回ってりゃ目は回る" (spin round and round and your eyes start spinning). They don't know the face of the person next to them, and the crowd is so thick they can't see ahead. That is the city in two lines, and it is pretty accurate.
The singer's answer is to throw themselves in anyway: "この身一つを投げ出して" (throwing in nothing but myself), tossing out "キザなセリフ" (cheesy, show-off lines) like cheap goods, because they want to touch and see Tokyo. There is a rough, street feel to the grammar here. Words like "知らねえ" and "見えねえ" are slangy, masculine versions of 知らない and 見えない, and "ラチはあかねえな" is a set phrase meaning "this is getting nowhere." The line about swallowing your spit to protect yourself is a nervy, gulp-and-keep-going image.
Then it flips into a night escape. Slipping into the dark, the singer heads off to see "あなた" (you), fed up with "眠れない街の 無意味な空騒ぎ" (the meaningless fuss of the city that never sleeps). The hook "君とトーキョーランデブー" just means "a Tokyo rendezvous with you", with ランデブー borrowed from French. Even the 満員電車 (packed rush-hour train) comes back, but now there is someone at the end of the line, and the chaos feels like something worth running through.