If the plane is not ETOPS certified it is likely that the plane is maintained under a far relaxed procedure. What the hell would happen if another engine fails? Even if the plane is certified, if it's not maintained to ETOPS standard there is still a higher chance of that happening.
By your mean this plane should just fly further even when the chance of second engine also failing is likely to be higher than ETOPS planes? And deliberately choose to ignore SOP is FINE, right? Jesus, if you're a real pilot I seriously doubt how you passed all your exams and line checks.
I kinda understand your logic, and would certainly hope (and expect) professional ATP's to adhere to correct protocol and ops for ETOPS (although that's up to the routing and type of flight, which equipment they give you, etc).
HOWEVER, having said that - I think your understanding of ETOPS is slightly flawed. There is no "relaxed maintenance" on the same aircraft which do not have ETOPS ratings - as others have said, there's simply a TON of paperwork and additional training for the mechanics and operations staff (and pilots, etc) some of which is established by the airline, and some directly by the FAA.
Yes generally the airlines training and some of the FAA protocols involve deeper inspections, but I wouldn't imply that any specific part can be neglected or treated any differently than a non-ETOPS plane. If the mx and service manuals say a part or piece needs to be a certain way - it still needs to be a certain way.
Granted I will give you the benefit of the doubt that said part possibly has a minute chance of not being seen, given non-ETOPS mx schedules/depth - but this is totally hypothetical.
Also I think the overall point here is that the air frame and engine combination is really what is "certified ETOPS" to demonstrate the required redundancy involved in that certification. To obtain and retain the rating requires airlines to do the above (mx procedures, training, etc) and report stats on aircraft performance. They also must have complete information on single-engine ops for all phases of flight and supply them to both the air and ground crews. Again we are talking paperwork and ops, not necessarily hardware.
It's not something we are talking about making a habit of, but I think the simple point here is that that airframe and engine combination has been PROVEN reliable and ETOPS-capable.
If (with fuel burn, time to run checklists, etc) the crew deemed that the negligible increase in flight time was not only possible, but may result in a safer outcome for the crew/pax, and possibly (as a secondary consideration) a far more economical choice for the airline (pax and mx) - then I see absolutely no problems with their decision. Again, we're talking a few minutes here, not 180 as some of these birds are currently rated for.