The rich (in Real Money) can afford the computer systems to dedicate to mining to become richer (in BitCoin).
Right now the miner's profitability is at a higher level than it has been but let's say that this level is a constant for the purposes of this discussion.
So Bob the miner spends today $1,000 on (used) hardware, and gets 1.4 Ghash/s.
He'll earn 0.6 BTC per day, worth about $3.84 at the current exchange rate ($6.59).
His electricity for that rig (725 Watts) costs $2.61 per day, so his gross profit is about $1.23 per day (or 0.2 BTC per day).
Assuming the exchange rate and difficulty do not change over the next one year period, Bob will have taken in about $450 worth of gross profit.
Let's say he then sells his rig, at $800 (just 20% discount for being used another year), and is left with $250 worth of net profit.
So for a $1,000 investment, Bob got a 25% return. This is not including his time invested.
In this example, Bob did better at mining than using that $1,000 to buy bitcoins outright.
But this is assuming the exchange rate didn't change.
Let's say instead over the next year the exchange rate went up a little over 50%, from $6.59 to $10.00 but let's also presume that the difficulty rises so that the profitability stays at about the same level it is now.
Presuming Bob sells enough bitcoins each month to pay for his electricity costs, he'll have roughly the same 0.2 BTC in profit per day. So one year later, Bob will have the 0.2 X 365 = 73 BTC in profit, but at $10 per BTC that is a year from now worth $730 USD.
And at the end of the year his equipment can be sold for $800, so subtract $200 from the profit, leaving Bob with $530 for mining, or a 53% profit on his $1,000 investment.
Next take Joe the speculator. Today Joe simply buys $1,000 worth of bitcoins -- at $6.59 he gets about 150 BTC. A year from now at $10 per, his stash is worth $1,500 so he profited $500, or about 50%.
Bob went through the effort to mine, including the acquisition and disposal of equipment over the one year and came out no better than Joe. The reason Bob did no better than Joe was because Bob's $1,000 was invested in hardware that doesn't gain in value.
If the exchange rate were to have gone even higher, Joe the speculator would have made more profit (and a greater ROI) than Bob the miner.
Now what happens in practice is that network-wide the mining capacity lags price so if the exchange rate goes up there are periods of time that margins for mining are generally higher. But if Bob is in Bitcion for the long term he actually would prefer the exchange rate not rise, at least not while he still is invested in the hardware. This also means that when the exchange rate drops quickly, miners are better off shutting down so as to not lose money on electricity.
The point of all this was to show how if the exchange rate goes up, speculating does better than mining. If the exchange rate goes down, mining does better than speculating. Mining can still lose money, but you can lose it a lot faster from pure speculation.
So this "rich get richer" has nothing to do with being able to buy the (relatively) expensive equipment that has caused a high barrier of entry that excludes the poor from mining. Mining is quite simply just a less risky form of speculating on the bitcoin exchange rate.
But for putting money into speculation, you are exactly right. A person who has only $25 to speculate will only get $25 richer if the exchange rate doubles. Where the person who buys $1,000 worth of bitcoin will become a $1,000 richer if the exchange rate doubles.
But for the poor there is no barrier to entry for speculating. You can buy $50 worth of bitcoins and pay nearly the same rate as that a wealthy person who speculates would pay, for example.
This cuts both ways though.
Eight months ago when the exchange rate was under $3 there were still people calling bitcoin a ponzi and complaining about those who were lucky and got in under $1. But they weren't expressing concern over those who had bought at $30, $15, $8 and $5 who remained underwater yet or had sold at a loss. There still are many people holding bitcoins today who are severely underwater on them yet. Just as the wealthy tend to gain more (dollar gain per capita) on the way up. that same subset of the population were the ones who mostly saw losses on the way down.