There will be a number of interlocks that sense door closed, door catch etc., to [prevent stupid people starting the microwave whilst there is any chance the door is not properly closed.
I suspect the missing catch part on th edoor will have a corresponding interlock switch inside the microwave itself.
You may be able to search for and find Delonghi spares. Give it a try - you never know but I doubt you'll be able to find a complete door or part of a door.
It'll probably mean a new microwave.
The good news is that microwaves are not that expensive and anything you do buy should have a decent warranty.