No, jet aitcraft do not have a "critical engine" in the same way as prop aircraft, in which the thrust is not symmetric about the centreline of the fuselage.
This is caused by the aerodynamic effect of the prop, in which the downgoing prop blade produces more thrust than the upgoing one. Hence, on an engine with the prop rotating clockwise (seen from behind looking forward) there is more thrust from the right side than the left.
So an aircraft with two identical engines (designed as above) will, in the event of the left (#1) engine failing, experience more assymetrical thrust than in the event of the right engine failing, since the left engine has more of its thrust closer to the fuselage. Therefore the left engine is referred to as the "critical" engine.
If the props rotate anti-clockwise, the right (#2) engine will be "critical". There are many aircraft out there on which the props rotate in opposite directions. These, therefore, have no "critical engine".
Depending upon the design of the systems (mainly on older aircraft) some jet aircraft will experience different problems with loss of aircraft systems, with ease of restart, etc. if this engine fails instead of that one. But this is not referred to as a "critical engine" problem.