Americans do not share a common culture or history. We share a political system that is at least in theoretically based on guaranteeing the freedom to participate in whatever culture you want, that isn't limited to people of a specific historical association (either by genetics or citizenship).
> the English race
While England does have a history and culture that traditionally was officially established by the king, Merriam-Webster's use in
this example can apply when referring to historic England, the term isn't really appropriate for modern England.
However, in Merriam-Webster's defense, this mildly misleading definition might be an attrempt to keep explanations simple with references young people would know. The definition that you copied was from the "RACE Defined for Kids" section of the page. Their recommended definition at the top of the page doesn't have the same issues:
1 : a breeding stock of animals
2 a : a family, tribe, people, or nation
belonging to the same stock
b : a class or kind of people unified by shared interests,
habits, or characteristics
3 a : an actually or potentially interbreeding group within a species;
also : a taxonomic category (such as a subspecies) representing
such a group
b : breed
c : a category of humankind that shares certain
distinctive physical traits
Most of these variations refer to what we now know is genetics. Isolated groujps of a species experience genetic drift (and other effects) that create genetic features unique to each group. Eventually the differences are large enough and we call them separate species (see: Darwin and the entire field of study that followed we call modern biology).
None of that applies to "Americans" as a group of people. We are famously a "melting pot" where people from very different races (again in theory) are supposed to have the freedom to "melt" together however they desire.
For a different but useful definition, from the Crown Prosecution Service in the UK:
> The Act says a "racial group" means a "group of persons defined by reference to race, colour, nationality (including citizenship) or ethnic or national origins."
noun
Definition of race for Students
1 : any one of the groups that human beings can be divided into based on shared distinctive physical traits
>>> 2 : a group of individuals who share a common culture or history the English race <<<
3 : a major group of living things the human race
https://www.merriam-webster.com/dictionary/race