You're missing a piece. Yes, you go up a short bit from the tracks to the bridge level, but you do not go towards the terminal, you go into the garage, which is towards the station. If you want to be super efficient, instead of going to the right to the closest elevator bank (which is going slightly away from the station), go left to the next elevator bank and you're going toward the station. It's also a simpler route for someone not familiar with the airport. Only the piece about going to the garage elevator is unsigned. Once you get out of the elevator in the basement under the garage, everything is well signed. Going through the hotel isn't a route I'd recommend for someone new to the airport.
Whoops, I could have been more clear. The signed T2 route involves going into the terminal, the T3 route through the garage doesn't but does involve the up-then-down.
I obviously wouldn't recommend any unsigned route to a newbie -- I'm trying to my optimize my own route for ORD int'l arrivals.