Yes.
But part of it is historical, too. Kroger has been a grocery store for decades. Lately, some of their stores have gotten bigger and they sell more stuff - like lawn furniture, small electronics and whatever. But they are still a grocery store because that's still their primary business, the stores are still organized like grocery stores (the way the aisles and departments and checkout lines are laid out), and that's how people think of them.
Walmart was a general goods store for decades. It didn't sell groceries. Lately (well, for the last several decades), they have added grocery departments but they aren't a grocery store. They are laid out like a general goods store and have all the departments a general goods store has (electronics, clothing, sports and outdoor equipment (including hunting-related goods in some areas), household goods, a pharmacy, a jewelry department, an automotive section, a pet section, etc.) They just decided to add groceries as another way to make money. But they aren't a grocery store or a supermarket in the traditional meaning.
You could say the two types of stores are converging (to some extent) but they are still noticeably different. They doubled the size of our Kroger but it still doesn't look or feel anything like a WalMart.
OK, so even though groceries are only a small part of the merchandise sold there
In the sense of the standard phrase
I need to go grocery shopping, groceries covers anything you eat (in my mind) including the meat and fish and fruit and baked goods and everything else. So I wouldn't say it's a small part. It's their main business.
Here's a typical grocery store layout:
Grocery Store Aisles Map Google Search Storage Pinterest Storage Cool Ideas 6149 | thehappyhypocrite.org
Almost everything is in long, parallel aisles
Here's a typical (newer) WalMart layout (click on the picture):
Weblinksnewsletter: Severn Maryland WalMart Opens - Well Received!
Things are divided up into rectangular, thematic sections by aisles