First-World Countries Do Not Necessarily Impoverish Third-World Countries By Making Themselves Richer

I 'technically agree,

But when a country is richer, it probably has citizens with more capital to buy up businesses and land in other countries,
Has the ability to monopolize trade,
Have largest share of X research, best schools.

Of course other countries wouldn't 'have to let the richer country do as it likes,
And they can take advantage of some of what the richer country offers them, before reapplying the benefits to themselves.
Foreign investment can be contracted to be temporary before returning to the invested in countries government or people.