For example when they keep printing their national currency, they devalue that fiat and consequently price of everything goes up against their fiat.
The only case where dollar comes in is when that other country is an importer of US inflation. In simple terms that is when US prints dollar out of thin air and purchases real goods and services from that country.
Now, granted bitcoin has created great opportunities for a small number of individuals in different countries to make some additional money and improve their own personal financial situation, but as a whole it is not affecting the economy at a large scale.
It makes sense because there are countries who have sanctions imposed by USA and still they are doing good because they are producing stuff internally and not much dependent on imports, for which you need USD. As long as government is determined on self reliance, the USD monopoly cant affect the country economy.
US government is free to print as many USD as they like since it's backed by nothing. Unless the USD printing machine is working fine, US government can print USD currency notes there is absolutely no limit of it.
Bitcoin is in its very initial stages and right now its impact is on individuals. We need to wait and see whether it can have any impact on economy on large scale in the long run.