Sure.
Nothing you've quoted indicates any requirement for en-route alternates to conform to any particular weather minima if the flight is non- ETOPS.
Can you quote anything that would, say, cause a re-route or cancellation to be required because any or all en-route aerodromes, within the 60 minute ETOPS threshold, was below any particular weather minima? Yes, you should know what the weather is like at aerodromes on your route, so you know whether they are available to divert to, but there is no planning OR en route minimum weather that they have to conform to to commence and continue the flight, as long as the flight is non-ETOPs.
You can fly 10 000 miles over nothing but aerodromes that are 0/0 in fog, as long as you are never more than 60 minutes from an Adequate Aerodrome, the definition of which does not include any weather requirements.