How can a culture which does not have those values (specifically, the ones around scientific method, work ethic, and future orientation) compete against one which does, in a modern industrial/technological society?
You're right - a society without scientific method or future-orientation will not develop industry and technology to the same extent.
But note how your question presupposes that competition is the only viable form of coexistence - or, at least, the only one that matters. But competition only occurs when at least one of the participants is acting competitively (i.e. treats the whole thing as a zero-sum game with winners and losers). If all players decide to collaborate, or even simply to coexist, why would a conscious choice resulting in a lesser degree of technological development be considered problematic? And if it's not problematic in that hypothetical arrangement, then what is the actual source of the problem IRL?
I agree, it wouldn't be problematic, but it seems like a world-scale prisoner's dilemma, that goes back at least to the time of the dawn of agriculture. All it takes is one culture to defect, and they will "win" - so how could you possibly disincentivize that?
Well, consider our own society. A perfectly natural way to outcompete your neighbor is by getting strong enough to murder them and take over their resources. But we have mechanisms that prevent this from being the norm.
When it comes to interactions between cultures, such mechanisms are still nascent. But since we're one of the cultures that have historically been defecting in this sense, the onus is on us to develop those mechanisms. We are in a unique position where we can take all those gains from unrestricted competition we engaged it, and utilize them to prevent the same in the future. And, conversely, if we treat other cultures as inferior on the basis that they couldn't (or refused to) remain competitive against us, that's straight-up victim blaming.
As for the counter-argument that if it weren't for us, they'd just be outcompeted by someone else, well... would you consider it acceptable to murder a person for material gain, if you knew with absolute certainty that they'd be murdered later by somebody else, anyway? Our society in general certainly does not consider this a valid justification - whatever the hypotheticals, the person who actually committed the murder bears full responsibility for it. If somebody were to say that the victim had it coming because they weren't able to muster an adequate defense, or because they refused to defend themselves for moral reasons (e.g. pacifism), that would be considered a morally repugnant position, right? So then isn't it hypocritical to not use the same logic for moral judgments on how our culture interacts with others?
In a world where resources (and / or distribution to them) are outpaced by the needs and wants of people, then interaction in the form of competition or cooperation is necessary.
Given that not every need or want can be fulfilled, they have to be prioritized in some way.
People with differing opinions on the value of fulfilling a particular need or want are going to have difficulty cooperating; a competitive system enables people to build up resources to fulfill their own needs and wants as they desire and are capable.
Societies have often found a way to balance these- markets for the majority of cases, and charity or taxation to fulfill the rest up to the point where they peacefully agree to do so.
A purely cooperative society, as you pointed out, works up until someone opts out. It is a fantasy.
It is not claiming that the bullet points are exclusive to white culture. It is claiming that they are associated with white culture and that they have become normalized in the United States because of this.