The Merriam-Webster definition for the verb equal is:
equaled or equalled; equaling or equalling
Definition of equal (Entry 3 of 3)
1 : to be equal to
especially : to be identical in value to
2 archaic: EQUALIZE
3 : to make or produce something equal to
If you scroll down the page, you'll see the heading Recent Examples on the Web: Adjective.
Under that is a See More (+) link.
Click on that, and many examples of the verb equal will be seen—including the example in question:
Recent Examples on the Web: Verb
// My family would do occasional vacations and stay at hotels, so to me a hotel equaled a vacation; hotel stays were immeasurably fun as a result.
— Mark Ellwood, Condé Nast Traveler, "The Stories of IRL Eloise: People Who Live in Hotels," 30 Nov. 2018
// The $345,300 Ferrari 488 Pista and $293,200 Porsche 911 GT2 RS equal its 0-60 mph time of 2.7 seconds.
— Basem Wasef, WIRED, "McLaren's $958,966 Senna Hypercar Ain't Pretty, but It Can Whip a Track," 30 June 2018
// That map also showed that the regions of Tampa Bay, Daytona Beach and Palm Beach County stood as more or less equals as the nation’s champs of lightning.
— Kevin Spear, OrlandoSentinel.com, "Florida loses reign as lightning leader to Mississippi," 26 Jan. 2018
The first two examples above are clearly verbs. They describe the actions of one thing equalling another.
But in the example in question, equals is not actually being used as a verb.
When used as a verb, equals is used in the following manner:
X equals Y.
But here is a simplified version of the example sentence in question:
They stood as equals.
In fact, if you look at the heading Recent Examples on the Web: Noun, you'll see the following example:
// In one oil sketch here, a trapper and Indian guide, the exhibition notes, appear as equals on horseback.
— Edward Rothstein, WSJ, "‘Albert Bierstadt: Witness to a Changing West’ Review: Where the Sublime Joins the Melancholy," 25 June 2018
This appear as equals construction mirrors the stood as equals construction from the example in dispute.
Since the same construction (both syntactical and semantic) can't be used for both functions of the word, the categorization of one of the two examples must be in error.
In short, Merriam-Webster made a mistake in including the example you raised in the section reserved for verb usage. It's being used as a noun and should have been put in the noun section instead.
As to your point about it being an adverb:
"How did they stand?"
"They stood as equals."
Here, as equals is acting as an adverbial phrase, but the word equals is, itself, a noun.
Compare it to this:
"How did they drink?"
"The drank like fish."
Here, like fish is also being used as an adverbial phrase, but the word fish is, itself, a noun.