Does this mean that is I sell DOGE on Kraken, that only buyer's on Kraken can purchase it? So someone on Bittrex cannot buy DOGE from a seller on Kraken?
Yes this is correct - in fact, what you can do is if you see doge is say 20 satoshi on Kracken and buy like 100000000 doge, then turn around and sell it for 24 on bittrex a moment later after the transfer clears .
This is called arbitrage. Not illegal, just a very unique thing in markets as it really just plays off of liquidity. Usually smaller exchanges end up with less liquidity and thus worse prices depending on the crowd/market