$4.8 million worth of Bitcoins traded in one week (in the United States alone), comes to around $690,000 per day, which is equivalent to some BTC3,000. Major exchanges such as BTC-e, Bitstamp, Bitinstant, and Kraken deal with many times this amount every day. So I have to say that although this might be an internal record for Localbitcoins, they have a long way to catch up to the major exchanges.
I guess we should take their daily/weekly volume with a pinch of salt. Just look at their 24H chart
https://bitcoinity.org/markets/localbitcoins/usd