Is jumping on a trampoline, considered good sport activity for childrens?

Ask him what he would like to do. At his age the social side is probably just as important. Is he a team player? or more solitary? Plenty of football/rugby clubs about or if he is more into individual sports then it could be boxing or judo. Many fitness set ups do circuits for children now...a great way to test himself and make friends.
Just jumping up and down on a home based trampoline sounds a tame to me.

Find out if local authority run classes with a professional in charge. Safety first.

I did trampolining during PE at school and I can quite honestly say, you use muscles you don't realise that you have!
However there is still a need for a social aspect needed to be taken into account. There must be a football/rugby/ scouts group or team around he can join which I'd have thought would be better for him.
On the safety bit - one of our neighbour's trampoline , in recent strong winds, was blown over her 7 foot (2 metre) high fence, landing in the middle of the road!

This is from a newspaper article in 2017:

"Last week, the BBC obtained figures which showed that in the year to April 2016, 315 ambulances were called out to 30 trampoline parks. The Flip Out park in Stoke called out an ambulance about once a week; its branch in Chester is under investigation after three people reportedly broke their backs in one day after jumping 4m into a foam pit. Usually a warehouse-style building, filled with trampolines linked together, the parks are relatively new to the UK, but the sector is growing rapidly. There are now about 150, with an estimated 10-15m visits a year. In that context, the number of injuries is low, but they can be severe – there have been head injuries, and broken backs and necks.

"In the past decade, trampolines have also become an increasingly common – and controversial – garden fixture. The American Academy of Paediatrics has said parents should not buy one for their children because of the risk of injury; the Canadian Paediatric Society says the same."

Our grandchildren have a trampoline in the garden. I think it they are used sensibly they're probably OK - after all, there's a risk to almost any activity we do. However, some children (and my granddaughter is one of them) tend to be very enthusiastic and impetuous, not seeing the dangers that others do. It is concerning.

Trampolining is fine when attending a properly organised class under the control of a British Gymnastics qualified trampoline coach. Using a trampoline any other way is highly dangerous.
Trampoline Parks (as can be seen by the article from Elothian) are highly dangerous. Garden trampolines result in many attendances at A & E (ask any A&E Consultant what they think about garden trampolines), whilst most of these attendances are for such breaks as arms and legs, etc, some are seriously life changing.
Even those parents who think they are supervising their children on garden trampolines cannot be there all of the time. More than one person on such a trampoline is an accident waiting to happen.
It is great exercise and good fun, but needs to be in a proper place, with proper equipment and qualified coaches.

At that age my Grandsons had grown out of trampoline , they are more into cycling , Scouts and just hanging about !