In order to see the errors here you need to focus on the core of the sentence. Look for the main subject and verb by pulling out the modifying elements.
The proliferation
of computer games designed to involve many players at once were
firstdeveloped
before the widespread availability of high-speed internet connections.
The core is: The proliferation were developed.
Clearly there is a subject/verb agreement issue here because proliferation is singular and were is plural. There also seems to be a meaning issue because of the use of the passive voice, which make more sense with computer games that it does with the proliferation.
Two potential fixes for the verb issues in the sentence:
The proliferation of computer games designed to involve many players at once
were first
developed before the widespread availability of high-speed internet connections.
The proliferation of Computer games designed to involve many players at once were first
developed before the widespread availability of high-speed internet connections.
KW