If we're doing Wikipedia as the sole citation then:

In 1806, Webster published his first dictionary, A Compendious Dictionary of the English Language. By 1807, he began work on a more extensive dictionary, An American Dictionary of the English Language, which took twenty-six years to complete. To evaluate the etymology of words, Webster learned twenty-eight languages, including Old English, Gothic, German, Greek, Latin, Italian, Spanish, French, Dutch, Welsh, Russian, Hebrew, Aramaic, Persian, Arabic, and Sanskrit. His goal was to standardize American English, which varied widely across the country. They also spelled, pronounced, and used English words differently.

https://en.wikipedia.org/wiki/Noah_Webster#Blue-backed_speller

As time went on, Webster changed the spellings in the book to more phonetic ones. Most of them already existed as alternative spellings.[34] He chose spellings such as defense, color, and traveler, and changed the re to er in words such as center. He also changed tongue to the older spelling tung, but this did not catch on.

Furthermore your quote doesn't actually have a relevant citation:

He was very influential in popularizing certain spellings in the United States, but he did not originate them. Rather […] he chose already existing options such as center, color and check for the simplicity, analogy or etymology”

Though in context of the previous paragraph seems to imply that this was an opinion that the wikipedia article came to simply because there was a previous work that argued specifically for 'or' in place of 'our' but again, it appears to simply be their opinion based on an assumption.