In the books, the pieces get knocked unconscious, not smashed.
Hermione’s knight gets taken off the board, not smashed, when Ron captured it. He’s wrestled off his horse and dragged off the board, but overall fine.
“Harry fretted about this next to the fire in the Gryffindor common room, while Ron and Hermione used their lesson off to play a game of wizard chess.
‘For heaven’s sake, Harry,’ said Hermione, exasperated, as one of Ron’s bishops wrestled her knight off his horse and dragged him off the board. ‘Go and find Justin if it’s so important to you.”
- Harry Potter and the Chamber of Secrets, Chapter 11 (The Duelling Club)
During the giant chess game in the book, the opposing queen takes out Harry and co’s knight. The knight gets knocked out and dragged aside.
“Their first real shock came when their other knight was taken. The white queen smashed him to the floor and dragged him off the board, where he lay quite still, face down.”
- Harry Potter and the Philosopher's Stone, Chapter 16 (Through the Trapdoor)
It doesn’t seem like the most pleasant experience, but he’s certainly still intact, just not conscious at that moment.
In addition, chess sets certainly aren’t “one-time use” items.
Ron had a chess set which he’d gotten from his grandfather and had been using for a while.
“Ron also started teaching Harry wizard chess. This was exactly like Muggle chess except that the figures were alive, which made it a lot like directing troops in battle. Ron’s set was very old and battered. Like everything else he owned, it had once belonged to someone else in his family – in this case, his grandfather. However, old chessmen weren’t a drawback at all. Ron knew them so well he never had trouble getting them to do what he wanted.”
- Harry Potter and the Philosopher's Stone, Chapter 12 (The Mirror of Erised)
Since it’s made clear that Ron has been playing with these chessmen for a while, it’s also proven that wizard chess sets can certainly be used more than once.
In the movies, they’re likely repaired magically.
It’s possible, even though it’s never shown onscreen, that the chessmen have some sort of magic that automatically lets them repair themselves. In addition, a spell like Reparo would very likely work.
“Ron!’ said Hermione reproachfully, and she pulled out her wand, muttered ‘Reparo!’, and the glass shards flew back into a single pane, and back into the door.”
- Harry Potter and the Goblet of Fire, Chapter 11 (Aboard the Hogwarts Express)
Reparo fixes broken objects, so it’s likely it’d work on the chessmen, or that there’d be a similar spell that would.