ChristianJ: you don't fly an oil pressure gauge, but you need one nonetheless to tell you what's going on.
See also the AoA gauge, in an airliner's cockpit, a good cross check in certain situations so you know what's going on.
But Zorin made a decent point: with what looks to be a scan breakdown among two pilots, who would the AoA gauge have helped? Most likely the Captain in this case, as he entered and tried to suss out the problem.