What happened to my steak?
There are many variables here that may or may not caused OP's problem.

The Pan sounds as it might not have been hot enough.  How hot was quite hot, how long could you hover your hand above the pan? 
Did you notice any change to the oil once you added it to the pan, did it streak, did it start to smoke?
[Personally I tend to oil the meat before placing into the pan.]

I think the main flaw is the frying for a minute on each side, at the temperature you had, that cooking time was too low.  Maybe 2-4 minutes on each side.  A medium should have a lot more heat penetrate the edges and allow that heat to transfer and cook the steak off the heat.

That's an acceptable blue/rare steak though.