by the very definition of the word
Everyone has their own definition, or cherry picks a definition they find somewhere to fit their own definition, so this is an irrelevant argument. If we all agreed on a definition, there wouldn't be a debate lol.
Sport (British English) or sports (American English) includes all forms of competitive physical activity or games which,[1] through casual or organised participation, aim to use, maintain or improve physical ability and skills while providing enjoyment to participants, and in some cases, entertainment for spectators.[2] - Wikipedia page for Sports
[1]"Definition of sport". SportAccord International Sports Federation. Archived from the original on 28 October 2011.
[2]Council of Europe. "The Europien sport charter". Retrieved 5 March 2012.
Unfortunately there's no substantiation for what 'physical' is, or 'skill', which imo doesn't disqualify video games. And that's the trouble of 'by definition': definitions need further definitions to make sense - otherwise we're just using our own bias to reafirm our own biases.
You cited merrian-webster dictionary.
This cites two international sports authorities.
I'm not saying either is wrong or right, I'm saying its easy to find a definition that exactly matches what one is arguing, which again makes it irrelevant.