Not an Intel recruiter, but I've placed engineers there and talked to enough hiring managers to give you the real picture.
Intel's behavioral framework is not as flashy as Amazon's Leadership Principles system, but it's real and consistent. The core themes that come up across teams:
Cross-functional collaboration. Intel is a massive company. Hardware, software, firmware, manufacturing, and platform engineering all have to work together constantly. They'll ask about times you worked with people who had very different technical backgrounds from yours. If your answer is entirely about working with other SWEs, you'll score lower than you should.
Navigating ambiguity in technical decisions. They want to see that you can make a call with incomplete information and defend it. A classic question: "Tell me about a time you had to make an important decision without having all the data you wanted." They care about your decision-making process, not just the outcome.
Inclusion and respect. Intel has been investing heavily in this area. Expect at least one question about how you handle disagreement with a peer or manager, and how you create space for different perspectives. This is not a gotcha, they genuinely care about it.
Impact and ownership. Standard stuff but Intel frames it around long-term product bets. They're a slower-moving company than a startup and they want people who can sustain focus on a project for 18 months, not just sprint and ship.
The format is usually structured STAR questions with follow-up probes. Three to four behavioral questions in a dedicated round, plus behavioral questions woven into the hiring manager chat.
One thing that surprises candidates: they often don't ask about failure explicitly as a standalone question. They'll probe for it through follow-up questions within a success story. Be ready to share what didn't go perfectly even if they don't ask outright.