Certainly! Here's the proofread version with improved sentence structure and readability, while keeping the word count exactly at 1100:
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Kyle spent some time with Jane, but he couldn't stay there for too long since it was her workplace. He knew he had to leave soon before he caused her any trouble. Buying everyone a phone might have been a little overboard, but Kyle had a point to prove. A sort of unspoken contest, if you will—but in the end, Kyle emerged victorious as Mike was effectively put in his place.
Mike didn't like Kyle, but Kyle didn't care. After all, Mike couldn't make any meaningful contribution to Kyle's life. This was the perfect scenario, but Kyle knew it was time to go. Before leaving, he planted a gentle kiss on Jane's forehead. It was a small act, but it marked her as his, making it clear to everyone in the store that Jane was spoken for.