I think everyone is looking too much into it. Although this is not a particularly funny far side (rare), the joke is quite obvious.

When you think of a refined person sitting and relaxing while he or she reads the paper, you picture him or her in a very tidy house with a bowl of fruit on the table. The opposite of what you'd expect is for an unrefined "brute" in a similar situation. Therefore this comic represents the irony of a neanderthal in an extremely messy and tattered house with a bowl of meat on the table (juxtaposition). I'm not sure the paper has anything to do with the joke but it is a funny addition that the neanderthal likely cannot read so why put words into it.

Gary Larson is brilliant but this is not one of his better Far Sides.