Patch and use a rug. This floor looks like it works fine. Or replace the entire floor with more of the same.

splice in a piece of a remnant of sheet vinyl...can you find beige from your flooring store scrap area? call the manager and bring them the pic w the exposed spot .....cut to fit/ cement it down / and stencil the beige geometric shapes with beige rustoleum paint ...scuff it / prime it w rustoleum primer and paint . itill be okay.. put a little mat in the area generally not too obvious / being straight triangle lines and only 2 colors .... I'd paint but you want it level so similar thickness sheet vinyl for that . its usually the grade difference that becomes the obstacle and leaves you w a problem. those colors would be easy .