Global warming affects all countries (although some more than others depending on the net costs of warming), but efforts to reduce emissions in a country are paid for by the residents of that country. So the government of a a country, especially a small country, is arguably not acting in the interests of its residents if it is taking the strongest actions against global warming. The same logic applies when states and even cities of the U.S. take steps against global warming.
Will countries like China and India reduce emissions just because other countries have set an example? I think they will pursue their interests more narrowly.
Your unstated assumption is that dealing with climate change is a cost, not a benefit.
So, you'd expect these selfish countries to adopt the bits of the program, that benefit them, and stall on the ones that cost them.
So e.g. if you import fossil fuels, you'd adopt renewables faster as they are cheaper, more predictable, more reliable etc. If you import oil you'd move to EVs, if you import gas you'd move to heat pumps and so on.
Efficiency would be prioritised, as would things that clean up local air pollution.
Will countries like China and India reduce emissions just because other countries have set an example? I think they will pursue their interests more narrowly.