"asl", or alternatively "A/S/L", was short for "Age/Sex/Location". This was a pretty common way of kicking off a 1-on-1 conversation on IRC back in the day.
Arguably it does make sense in the context of making a joke about 90's Internet slang as the author appears to be doing, but I agree it doesn't make sense as something you'd actually say to pause a conversation. On the other hand, it might actually have that effect...