Itagaki explained that the first PS2 release of Dead or Alive 2 (which only came out in Japan; the one at the US PS2 launch, DOA2 Hardcore, was a remake) was unfinished, and sent to manufacturing under false pretenses. A manager approached him and asked to borrow a copy of the in-progress game to play it. "Instead," he said, "it was taken into a factory for production on that day without me knowing it." The team only had two and a half months to work on it. "To be sure, the company made a huge profit."
The game had relatively low-quality, jagged graphics and a lack of extra content. Itagaki became depressed about the unfinished game. "I thought I would quit making games," he said. "Some of the staff, including me, were so depressed by this fact." In this state, he stayed home for "three or four months," drinking and repeatedly watching ... Armageddon, singing along to the sappy "I Don't Want to Miss a Thing" with his daughter, which he admitted was a "stupid life." "If I close my eyes now and recall Armageddon, tears still come out," he said.
So the secret to the Aerosmith songs in those DOA games is that Itagaki seriously, unironically loves Aerosmith. The real surprise is that Bruce Willis never made it into any of the games.