https://www.arlandaexpress.com/fares.aspx
2 for 300:-, 3 for 400 and 4 for 500:-
Christmas special: applicable everyday from Dec 14 to Jan 10.
Two, three or four persons travelling together, single journey. This discounted ticket cannot be rebooked or refunded. Can be purchased online and in our ticket vending machines, ticket counter at Stockholm Central Station and in the Information counters at Arlanda.

I tried booking return journey from ARN to Stockholm on April 4 and back to ARN on April 9. I am getting the discounted fare (2 for 300sek). My question is from the text above I thought travel dates should be between Dec 14 and Jan 10 and not the booking date. Can someone confirm?

I don't want to book it with discount even though I am getting discounted pricing on website for April 2016....Just wanted to make sure they don't void my ticket on travel day and I have to pay extra SEK.

I think you are getting cheaper tickets offered because you are travelling Thursday-Sunday.
https://www.arlandaexpress.com/fares.aspx

I tried booking tickets on other days than these and the discounted fare didn't show up.
And checking dates being Thursday to Sunday, the discounted fare showed up (with wrong info about validity as you also saw).

I went ahead and booked the discounted AE tickets for April 4 and 9 :-)