All of that notwithstanding, it is very possible and in fact extremely common for alpha traits to be displayed in chess, both the Machiavellian style and the more “woke” for lack of a better term. In a one on one game, this is communicated in the non-game communication ie body language. In a club or team setting all of the usual social dominance tactics apply.
Honestly I dislike using the term alpha, because it's so inflammatory. Its hard to talk about what alpha means without bringing up beta, and the moment you use those two words then it sounds like redpill-speak. However, there are certain kinds of people who are confrontational and very much extroverted, the kinds who don't back away when challenged. I see alpha as a way to describe these traits as they are, with no moral conclusions attached.
For sure Chess players can display alpha traits, but it's hard to see how Chess players are MORE alpha than Diplomacy players. An entire game of Chess can finish without a single word exchanged, and it's rare and unprofessional for violence to show up in Chess, though it does show up time to time. In diplomacy, violence, albeit only verbal, is the norm. A nonconfrontational person will never survive in diplomacy, but they can do well in Chess.
For that reason, I encourage you to stop conflating "alpha" with antisocial character traits. Words matter. The very idea that this is acceptable behavior for leaders, that sometimes violence is the answer, perpetuates the social norms that allow bullies to stay in power.
Also, your conception of diplomacy needs work. Again, anybody who is actually any good at diplomacy understands how it is possible to convey a firm position with minimal violence. Diplomacy is more of a dance. You don't want to be the kind of lead dancer who's violently swinging your partner around the room.
If you really believe that confrontation can't be resolved without violence, I recommend a meditation practice known as "metta" [compassion]. Reading the Art of War may also provide inspiration and guidance on this front.
It implies that humans are evolved to live in a hierarchical and purely competitive society which is known to be false (not only for us but for many mammals). Humans are not insect nor lobsters.
There are various books from prof. https://en.wikipedia.org/wiki/Robert_Sapolsky and youtube videos with good analysis of social behavior in primates including humans.
Go, and a lot of modern heavy strategy games are way more complex than Chess.
No disrespect to Diplomacy, I think it's a great game. However I would respectfully submit that chess might have a stronger claim to being "the board game of the alpha nerds". (Or go, arguably, in the eastern world. But despite go's supremacy in terms of complexity, it hasn't captured the world's imagination like chess has.)
There's a reason why chess scenes always pop up in movies and literature featuring, e.g. criminal masterminds vs Sherlock, or the venerable doctor teaching strategy to the protégé. The reason is, chess (rightfully or not) is universally recognized as the quintessential game symbolizing human intelligence.
In my opinion as a former competitive chess player, chess skill actually isn't correlated with general intelligence, in the sense that if you're smart enough to get good at chess, at some point you realize that there are more worthwhile things to be doing with your time. But that's neither here nor there.
My main argument is that if we did a vote among all the world's "alpha nerds" to determine who is the alpha-est and nerdiest of us all, I suspect that current world chess champion Magnus Carlsen might place higher than any of these Diplomacy masters. I have no idea how this survey methodology would work (could anyone declare themselves an alpha nerd, or would they need to be confirmed by other nerds with official titles in nerdy activities?), but you get my point.