It's tough for all vendors, there are just different situations. Large vendors should have the ability to get leaner rather than the alternative of losing their Walmart business. Smaller vendors -- especially new vendors -- can rationalize based on the incremental growth. The worst position would be for small incumbent vendor where there are lots of substitutions. Unless you have retail leverage on Walmart, you don't have much choice other than to adjust elsewhere in your business.
In-store may go down but I know that online can go up on Prime Day by virtue of more people being online shopping. Amazon trains people to shop on Prime Day like must-see TV. If more people are shopping online that day it could/should be great for online sales. When I was running sales for a primarily direct-to-consumer brand, we saw our sales increase on Prime Day not only on Amazon, but at Living Social, Groupon and our own website. Prime Day just became a second "Christmas In July" for us.
Now if I'm an omnichannel retailer I would charge my team to have our own "sub-prime" deals (like what I did there?) ready to go and promote on our website, social channels and email database. Heck I may even promote them in-store leading up to Prime Day. If they aren't walking in the door that day at least they know I've got something online.
If there are Black Friday and Cyber Monday websites that curate all the ads and deals, excuse me while I go register subprimedeals.com and subprimedealsday.com and start preparing for some nice affiliate traffic and commission on Prime Day next year!