There's an obvious difference
Your puppy
is not relieving himself in one end, and playing happily in the other. That may well be due in part to the water restriction. But also a likely factor is that he doesn't want to pee in his crate - even if he can get a small distance away from it.
The whole purpose of crates as housetraining tools is exactly that - they DO provide a significant disincentive to puppies relieving themselves. OK, for
some pups the need/desire to urinate is greater than the evil of having to sit in it - and their owner have to resort to things like removing bedding and putting in dividers. But that's not the majority (there may be many posts here about that sort of thing - but that's because people post when they HAVE problems, not when they don't). For most pups, just being crated is sufficient deterrent for a good period of time (eventually, every pup would have no choice but to pee, of course).
The bottom line is that your puppy isn't urinating for 6-7 hours daily. And that is not good for his health. Gated in the kitchen (for example) with his crate door open - he can sleep in his crate, drink whatever fluids his body requires - and urinate well away from his bed when he needs to. He is far more likely to relieve himself as needed in this case.
Now that may sound rather the opposite of what you'd like - your currently dry pup peeing in your kitchen. But the age of your puppy and the potential impacts of him (a) being dehydrated, and (b) holding toxins within his body for such long periods needs to be considered. At this age, he should be needing to urinate every 30 minutes or so. Asking him to hold on for up to 3 hours isn't the end of the world. But creating a situation with limited water and unable to urinate for 6-7 hours might be. He's liable to end at least with UTIs and undue stress on his internal organs.
Now, quite possibly, once you start leaving him with water, he *might* start peeing in one end of his crate. But believe me, you don't want that to happen
Not just because it's harder to clean up than some soggy newspaper - but because it would end with the puppy effectively trained to pee in his crate. And once he loses inhibition about doing that, it's an incredibly difficult thing to untrain and you can end with a dog who pees in his crate all his life.
The newspaper solution generally gets around all of that. OK, it would be an ideal world if you didn't have to use the newspaper, and could always be there to take your puppy outside to urinate. But that's ideal world - very few of us have that luxury. We just have to choose the best solutions we can that don't involve risk to the pup (nor creation of problems like a dog trained to pee in the crate). The best solutions available are thus
either finding/paying someone to come every few hours to give the puppy a potty stop outside, or else providing a place outside his crate where he can urinate on demand.
He only did it a couple of times. He eventually stopped peeing in the pen (on potty pads). He just tore up the pads instead. :( Your pup will eventually get it. It will just take a little longer.