Stoney is correct. "It was not a question for them being able to get a car" is not acceptable English. If it really did appear in a book, then the publishers need to find new editors/proofreaders.
In "It was not a question of them being able to get a car", 'being' is a gerund; it is a form of the verb, but has some noun-like qualities. This is why some purists would prefer 'their' to 'them'.
This is an extract from a quite technical document. In addition to the problem of understanding the English constructs, you have second challenge in that certain terms have specialised technical meanings. Here we see process being used in a very particular way, as well as processing being used in a subtly different but related way.
In understanding this passage you need to identify the technical terms and establish their meaning in this particular document. You cannot do this simply by reading this one paragraph. We would hope that there would be a glossary for this particular document that would define the terms, however there may well not be one, so instead we at least need to look at a technical dictionary (for example), we cannot simply appeal to standard English usage.
So here you need to know what process, web server, request, concurrent and processing mean.
From my own knowledge of this field the Web Server is a particular process running on a computer, there will be many such processes running. The Web Server has responsibility to receive requests (typically from a Browser) and performs processing to satisfy those requests.
Here we come to the meaning of on behalf which can mean in the interest or aid of. So for each request some processing is done, that processing is on behalf of a single request.
The key idea is that the Web Server is satisfying multiple requests at the same time concurrently. And the issue being addressed is what happens is one request's processing effectively monopolises the Web Server for a period of time, in this case the other requests, concurrently being processed are stalled until the monopolising processing is finished.
Hence to understand this paragraph we need to get definitions of some technical terms but also need some quite detailed technical background information about multi-threaded concurrent processing.
The only slightly tricky English here is the on behalf, which becomes clear when we understand the relationship between a request and its processing.
Best Answer
Without more context the meaning isn't clear; I'd rephrase it in one of the following ways, depending in part on intent.