The lockdown rules the country was under set these rules as a condition - you may leave the house only to exercise, and you may not travel to get to a place to exercise. This was to stop people going to tourist spots, petrol stations and other places they may interact with others.
You're right in a way - a single family doing it probably causes no actual harm because they're the only people present. Now - who gave this unelected government advisor special permission to go there and be that single family, while nobody else could, and was locked down hard?
He's so blatantly lying about the "eye sight test", it shows a total lack of respect for the public and his role as part of the UK government. They should be, if anything, following the rules more than anyone else in order to set an example.
Stated reasons were (1) reducing load on health services from road accidents (which has worked - my friend in A&E says he's "never sat around on his arse so much at work before"); (2) reduce transmission of virus at fuel stations, risk to breakdown services, etc
I feel for people stuck in apartments!
If I remember rightly, there was actually a bit of a controversy over this because the police in some areas got it into their heads that no-one should be driving to places to walk full stop and started pushing that message and complaining about people not following it, even though that wasn't actually a rule. Though it's entirely possible a lot of the media coverage of that has also been memory-holed and only exists in the Wayback machine; the BBC in particular have been completely rewriting articles a lot lately.
(The restriction to one session of exercise per day was also only legally enforceable in Wales and not England, for some reason, even though it was part of the advice in both.)
There was a law mismatch here. The government were saying you can't do that, however the legal powers they had (and the powers they delegated to the police) were not sufficient to actually stop people for some of the things they were stopping them for.
I think Derbyshire police were the worst for that.
So it's possible here that Dominic Cummings didn't break the lockdown laws, but he certainly broke the lockdown rules his own government were telling the public.
He drove from an area with high rates of Covid-19, with his covid-19 positive wife, to an area with low rates of Covid-19.
This is entirely the point of lockdown -- to reduce the spread of the disease.