You're on the right track. From the article:

"Costco pays a starting wage of $11.50 an hour, gives most employees healthcare and other benefits, and has not switched to the model adopted by many big-box retailers of using temporary firms in warehouses to keep costs low."

A higher minimum wage costs Costco nothing and hurts their competitors.

I wouldn't say it costs them nothing. If competitors are forced to raise their wages near Costco's, Costco either needs to up the ante or lose some of the luster they've created in treating their employees so well compared to the average retailer.

I'm not saying they don't have good business reasons for this, they do, but it isn't all pure business upside for them.

Some of the costs from vendors may also increase as a result.

In theory, that is a shared cost amongst all their competitors.

13 $/hr + 0.5$ raise every 300 hours worked up to about 18$.