I don't think the new Walmart will have any effect on Gene's. I go to Gene's for the quality of the meat and produce. Over the years I've noticed that Gene's prices for the standard grocery items like bread and milk are 100% in line with those from Lucky or Safeway, so I get those at Gene's too.
Trader Joe's has its own unique products and seems to have its own following. If Walmart has any effect on this store, I think it will be because of the two stores' proximity more than anything else.
Then there's Safeway. I was surprised that there was enough business to support two in-town Safeway's, along with the two in Dublin. The Safeways are new, spacious, and offer full-service items like soups, the deli, and pharmacy, and even gas for your car...the one-stop shopping that makes it convenient. If I'm coming home from work and I need to shop quickly, Safeway is a good bet.
Finally, Lucky. Lucky (and the parent Save-Mart) have positioned themselves as the low-price leader, and as such I think they will have the greatest competition from the Walmart grocery. A lot is going to depend on Walmart's prices and selection. Lucky has a pretty good selection of meats, fish, and produce, and if Walmart can match I think Lucky is in for a tough time.
So - I predict:
Trader Joe's and Gene's - no change
Safeway - decrease in business for their Santa Rita store, no change for their Bernal/680 store
Lucky - big change