That looks the sort that closes the door with just a spring! The sort that control the closing and also latch it have oil in and that stops slamming - if you try to slam the door it resists.
solve the problem. Most have adjustment for 'close' & 'latch' which control the speed at which the door closes to a point a few inches away from the frame, slight pause, then it closes completely.
A good clip or two around some little ears - if a gentle warning is not enough! LOL
An overhead door closer (as pete) describes would be the most suitable.
You can get a type of these that will 'soft close' the door in the last few degrees of its closing arc (difficult to slam under any conditions [except if badly worn]) - and I believe this type can also hold the door open at 90 degrees (if required).
If you Google -- overhead door closer (or closure) -- then you should be able to get one from good ironmongery/door furniture suppliers.
The one that you have found will not 'soft close' the door, and can in fact be adjusted to slam the door even harder than the kids can do - and the adjusting pins (hardened steel) have been known to snap and cause personal damage to oneself (speaking from experience - ouch, it hurt).
Think before you fit one - you may not want the door to always be closed - and it to be harder to open.
I think training the kids has to be the best approach. Along with - keeping dirty hands off walls - not dragging hands on wall when reaching for a light switch, etc. It ain't hard.
Alternatively -- when they are playing - use a wedge to keep the lounge door open so they can't close it.
Had one fly off when fitting a spring to next door's garden gate. Didn't bother to search the lawn for it - just made one from a 2BA ch. hd. screw - fits properly and won't go rusty and just tight enough to need a screwdiver to get it in. Prolly outlast the gate and the closer.
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