is there anything particularly wrong in this exchange?

Person A: "I pirate the software, because frankly these studios don't need my $20 to stave off bankruptcy"

Person B: "If everyone thought like you, they'd go bankrupt" 

Person A is giving a reason for stealing. The reason is essentially "If I do, the company from which I am steal will not go bankrupt." This reason is problematic for many reasons, mostly by giving a reason not typically associated with the reasons why people shouldn't steal. Call it a non sequitur if you wish.

Person B's response is also problematic. More accurately, what they probably mean is that if everyone did as Person A did, the company would go bankrupt. This can be a slippery slope fallacy. I say "can be" because they are not saying this WILL happen, but saying this to show the problematic nature of person A's reasoning. 

As an observer, I would have far more issues with person A's reasoning than person B's.

I see Person A's argument as an example of special pleading . It's pretty obvious to most people that software developers need some income in order to stay afloat, and they seem to acknowledge it by referencing a potential studio bankruptcy. So, they almost certainly know that other people are paying for the software in order to keep the company running, Person A just feels that they shouldn't have to because their $20 would be an insignificant amount compared to the company's operating expenses, but that's also true of everyone else who uses the software.

There seem to be some implied but missing steps in Person A’s argument.

P1: stealing is bad iff (i.e., iff and only if) it leads to bankruptcy – or – stealing is OK if it doesn’t lead to bankruptcy

P2: me stealing won’t lead to bankruptcy.

C: therefore, stealing isn’t bad.

even if we accept P2, I suspect most folks would consider P1 false.

Person B relies on a slippery slope, especially assuming “they’d” means “they would”.

The short answer is: if stealing only depends on whether someone can “afford it,” then you’ve justified mugging anyone in a nice suit — and being mugged yourself by anyone with less than you. The definition of rich by such people is anyone who has more than I have.
A longer answer is:
One error is the “justification by irrelevance.” He says, They don’t need my money, as though the moral status of his action depended on the victim’s financial condition. But theft—whether of software, goods, or money—is wrong for a deeper reason: it violates the principle of non-aggression, which means not initiating force or harm against others, and the principle of respecting the rights of others, meaning acknowledging and not infringing on others' property or freedoms.
When you steal, you are taking something that does not belong to you without the owner’s consent. That action is wrong regardless of the victim’s wealth or resilience, just as it would be wrong to steal a loaf of bread from a millionaire’s kitchen or a bike from a corporate CEO’s garage. The moral wrongness isn’t erased because “they can afford it.”
To put it another way: the ethics of theft depends on the nature of the action, not on the balance sheet of the victim. (Property rights, as used here, refers to the legitimate authority to use, dispose of, or exclude others from one's own possessions.) If the permissibility of stealing hinged on whether the victim 'really needed' the property, then property rights would evaporate for all. That principle would reduce to 'from each according to his ability, to each according to his desire,' which is simply a denial of rights altogether.
In case what I said is not clear:
    > Theft is wrong because it overrides the owner’s right to decide how the owner’s property is used.
    > The victim’s capacity to withstand the loss doesn’t change the fact that the thief has taken something that is not his.
    > To make wealth the measure of whether theft is wrong is to say nobody has any rights—which is itself unjust.
Beyond law and morals, theft hurts the community. If a producer suffers losses, he’ll stop providing goods. For example, if a farmer’s harvest is stolen and threatened again, will he grow the crop next year?