Can you give some details like how would he get out like fitting between the bars, a hole, crack, he picks locks, etc. for example mine knows how to open her door and get out of her cage.
Can you measure the width between the bars? If he could escape THROUGH the bars then it is definitely the wrong size--it's a parrot cage for sure! If he could just possibly get his head stuck and hurt himself (which is usually the concern), then we'd really need to know the actual width to know. If you are talking about opening the door then, looking at that latch in the second picture, yes it is possible he could figure out how to open it. My Quaker's sleeping cage has that kind of latch. I've found that BIG binder clips (the kind that hold a huge stack of papers) work well to keep him in. He's not strong enough to apply the pressure to squeeze it open even a little (though a big bird could make short work of it!) and unlike a lock it doesn't take long to remove. Can you get some better pics of the cage (like the whole cage) and also the doors?
If the bar spacing is large enough to get his head through, then I would pass on the cage.... The picture looks like it might be 1"? bar spacing, which is too big for a cockatiel.