It's philosophical terms. "One-boxer" and "two-boxer". "One-boxer" is dominated, "two-boxer" dominates. Comes from boxing. Two-boxer is the one who can hit strong with both hands. One-boxer has one can which is not as strong as the other.
In your context, it hits you with both hands, from up and down, from left and right, with hooks, with uppercuts, with jabs, etc...

A wild guess and maybe I'm just thick but I think she is saying that you need a lot of tissue to read this in public. Presumably the tissue is to wipe away the tears, although it could be to sneeze into because the book is mouldy, or to wipe the germs from all those icky public places that the book will be read in.

But I'll stop letting my imagination run, I think you had the answer all along.

See the site
Suppose that those members of the philosophical community who have both (i) thought seriously about Newcomb’s Problem and (ii) are familiar with the main arguments on both sides, are approximately evenly-divided between One-Boxers and Two-Boxers.[17] We can imagine various ways in which this state of disagreement gives way to a consensus. Here is one way: someone thinks of an ingenious argument that convinces all of the One-Boxers (or, alternatively, all of the Two-Boxers) that they have been in error up until now

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Note added at 43 mins (2004-01-22 07:37:39 GMT)
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the note give more details:

In his original presentation of Newcomb’s Problem, Robert Nozick wrote: “…I have put this problem to a large number of people…To almost everyone it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly” (“Newcomb’s Problem and Two Principles of Choice”, page 48). My sense is that the by-now over three decades worth of sustained debate on Newcomb’s Problem has resulted in a significant shift in the original distribution of opinion in favor of a policy of Two-Boxing. But I will abstract away from this fact in what follows: what is crucial for my purposes is simply that there are some actual defenders of One-Boxing as well as some actual defenders of Two-Boxing.

It means that the story is the sort that has you weeping buckets (bucketfuls of tears) at the end. So you should prepare extra (two boxes, in actual fact) paper tissues, so that you can mop up the tears that are bound to flow