Hampton Inns are owned by Hilton so they have a very high customer service index. If you really, really want to know about the chair I would try contacting the corporate office, give them the location and local phone number then tell them just what you posted here. I bet you will hear back from them, they are responsive to their customers. Here is a link that might be useful: Hampton Inn Contact Form

If you use your dining room for very casual family dinners, I suppose plastic molded chairs are suitable, but I prefer comfort over trend and plastic chairs are not terribly comfortable. What about something like these? (I know you said you were looking for white, but I thought this color was complimentary, too.)

That is patterned after - or may actually be - the Knoll Saarinen Executive Chair. Justifiably famous quintessential MCM chair. The wheels are on the desk chair version, but it also comes without wheels. You can upholster it any way you want, or choose one of the standard Knoll colors in leather, flat weave, boucle, or velvet. I saw them recently in a soft yellow the color of banana cream pie - to die for. These chairs will cost you a lot to purchase, and to upholster if you don’t want one of the Knoll fabrics, but you didn’t mention budget. The legs come in either metal or wood. For a kitchen dining table I prefer metal legs. For a dining room dining table I prefer wood legs. Here are links to them at Design Within Reach. There are likely cheaper knockoffs, but at least now you know the name to search for. https://www.dwr.com/workspace-chairs/saarinen-executive-side-chair-with-metal-legs/7214.html?lang=en_US#lang=en_US&q=Knoll+dining+chair&pn=2&start=2 https://www.dwr.com/dining-chairs-and-stools/saarinen-executive-side-chair-with-wood-legs/2260.html?lang=en_US#lang=en_US&q=Knoll+dining+chair&pn=2&start=3 In Knoll Swan Velvet: There’s also a version with arms:

Put your centerpiece on the chess table. Is the other ornate dining set for breakfast, gaming or could it be used here? Do you want to continue with the cow head/skin theme, leaning SW in your decor? They aren't really "cozy and elegant," IMO. Is a new chandy in the picture? That one misses the mark on elegance. You need a minimum of 36-42" from the table top to any baseboards or furniture surrounding the table to allow for chair sit/scoot space. I'd do that measurement first. I really wouldn't want the rug jammed up against the exterior wall. Maybe the smaller, round table would be a better choice for using a rug here.