I interviewed for 2 positions, "ASIC Development Co-op" and "ASIC Hardware Performance Modelling Co-op", I got an offer for the latter (Performance Modelling) but not for ASIC dev, so YMMV. They both took place on Cisco Webex, and made use of it's share screen feature as a critical part of the interview. I recommend some kind of digital drawing tool, I used an iPad & Apple Pencil synced to OneNote, opened up OneNote on my laptop, and shared that window.
Both interviews were similar and took around 80 min, albeit with different technical questions. There were 2 interviewers, one of who would be your direct supervisor, and the other is your supervisor's supervisor.
Initially, they spent a good 20 minutes explaining what they do at intel, and more importantly at their particular group within Intel (For those who don't know, Intel is internally split into operating groups, each of whom have a particular focus). I was interviewing for the NSG (Non-Volatile-Memory Solutions Group) group, so much of what was explained is the work they did on Intel's SSDs and Optane memory.
I was grilled hard on the single CompEng project on my resume (I am a CS major, and the rest of my resume was tailored towards getting an SWE job), where I designed a MIPS CPU from scratch (in Verilog). The interviewer wanted me to explain in detail how the CPU would execute instructions (as in the datapath/FSM), and the process of implementing it. This took around 30-40 min for both interviews.
The final portion were technical questions, aka "whiteboarding". The questions will be put below, and while they weren't difficult by any means, the clear focus was to see how you went about implementing them. I recommend talking through your thought process, and most importantly don't do hail mary's and guess randomly; Admit it if you don't know, these guys can tell. Pseudocode is okay, they don't expect anything to compile. My interviewer said he was particularly impressed that I wrote the 100 primes question by using an yet to be implemented function call that I implemented afterwards, so that the logic was segregated into nice readable chunks.
Overall, I felt a large portion of the interview was just them measuring your soft skills against your hard skills, as in are you able to clearly articulate a complex technical subject by processing it into comprehensible chunks. You do have to know your stuff (DS/A, Verilog, stuff on your own resume), but I felt that they wanted to see if you really understood your own answers more than anything else. No need to grind leetcode.