There are several reasons why these two firms can compete with each other without bankrupting one another.
1. Your assumptions may be wrong.
1.1. There are different ways firms compete.
Price competition is not the only way firms can compete. In the industrial organization literature, there are two basic forms of competition: price (Bertrand) and quantity (Cournot) competition. A mix of these two styles is also possible, and firms can switch between the two modes of competition.$^1$
In recent years many scholars started to also use term non-price competition because firms can also compete along numerous dimensions (e.g. market share, reputation and other).$^2$
In these richer models of competition it is not true that firms always price such that Price =Marginal Costs.
1.2. The products are not necessarily homogeneous.
One of your premises is that the products are homogeneous because they have the same technical parameters, but that is a mistaken premise. What matters is whether customers perceive these products as homogeneous or heterogeneous, not whether they physically are.
This often gets lost in translation because, outside specific sub-fields like industrial organization, textbook models tend to assume homogeneity or heterogeneity without elaboration. However, it is well known that firms can use marketing to make their products "stand out" and be perceived differently. For instance, in a Hotelling duopoly, firms can increase perceived differentiation and relax competition through advertising.
2. You are applying static model to evolving situation.
You are applying an insight from the static Bertrand model. That result assumes that the firms are engaged in a one-off, non-repeating strategic interaction. While this can be a good first approximation for an equilibrium that eventually arises:
We are clearly observing the situation from the vantage point of someone in the middle of it. How do you know that, in 20 or 30 years, AMD or Intel won't dominate most of the market?
Data from Statista show that until just very recently Intel actually had near monopoly over the whole market with almost 80% market share. Things changed recently, but this might be just a perturbation on a road to stable equilibrium with 1 firm.
Furthermore, once we move beyond static Bertrand, in dynamic Bertrand models, firms can recover the fixed costs of R&D investment. In fact, peer-reviewed research$^3$ shows that even in the presence of fixed costs, more than one or even two firms can exist simultaneously and earn enough profit to cover these fixed costs.
3. There could be some collusion.
It is always in principle possible that these firms collude and earn extra ordinary profit due to collusion.
However, this is difficult to judge without any rigorous research. Moreover, this thread contains misinformation/disinformation about how firms collude or US competition policy.
3.A. US policy actually allows monopoly if it can be shown to be good for customer. See the Federal Trade Commission own website that states this clearly;
Obtaining a monopoly by superior products, innovation, or business acumen is legal;
3.B. Moreover, government does not just acts against monopoly. FTC clearly states it can act also against duopolies. The number of firms actually is not directly part of FTC decision, and duopolies are already routinely investigated.
Consequently, it is misinformation/disinformation to claim that US government does not allow monopoly but allows duopolies. This is not how US anti trust policy works and it never worked this way in the past.
3.C. Institutional investors generally do not invest their own money (look at OECD explainer about institutional investors). As a result institutional investors do not directly reap benefits of two firms colluding.
Moreover, FTC actually tracks firm ownership so companies simply cannot cheat anti trust law by some third entity owning all the companies on the market.
As a result it is simply impossible to avoid anti trust in this way.
The two firms could tacitly collude through strategic interactions, for example, by using a grim trigger strategy$^4$. In this scenario, one firm keeps prices high and "plays nice" until the other firm deviates.
There are other ways to tacitly collude, but it is not possible to do so simply through ownership by institutional investors. The FTC can review board meeting minutes, subpoena witnesses, and more (FTC). As a result, when collusion remains undiscovered, it is typically tacit collusion. Any overt attempt to collude would be easily uncovered.
However, there is little evidence that AMD and Intel are colluding. The FTC actually prosecuted Intel for anti-competitive practices, but not AMD. In fact, its ruling was beneficial to AMD. This case demonstrates that Intel, not AMD, was engaging in anti-competitive behavior in the past, perhaps explaining its previously high market share. As part of the settlement, Intel had to implement policies that benefited AMD and other firms. Moreover, NBC reported that AMD filed a complaint against Intel, which contradicts the claim that these two firms cooperate. Why would AMD urge the FTC to act against Intel if they were colluding? This borders on conspiracy theory. The simpler explanation is that Intel had a superior market position, and AMD, as the underdog, was suppressed because Intel pursued anti-competitive practices that made it harder for customers to switch (see details of the case linked before).
This case also shows that the FTC does not focus solely on the number of firms in the market. They use various metrics to measure competition, which can differ on a case-by-case basis.
References:
Klemperer, P., & Meyer, M. (1986). Price competition vs. quantity competition: the role of uncertainty. The RAND Journal of Economics, 618-638.
Symeonidis, G. (2000). Price Competition, Non‐Price Competition and Market Structure: Theory and Evidence from the UK. Economica, 67(267), 437-456.
Saporiti, A., & Coloma, G. (2010). Bertrand competition in markets with fixed costs. The BE Journal of Theoretical Economics, 10(1), 0000102202193517041634.
Tadelis. Game Theory: An Introduction. 197-198.
