The type of export determines which records can appear with blank entries, so if you do a constituent export, you can export constituents who have no gifts, but if you do a gift export, you can't export constituents who have no gifts.
I assume that you are doing a participant export. In this case, you can export participants who do not have a seat assigned, but you cannot export seats that do not have a participant assigned, because the participant export requires a participant record.
In order to get what you want, you would need to start from the event record. Here's the bad news.
BB's support for events in general is awful. This includes not providing a way to export seating assignments from the event export.
Your only option is to access the data through the back end.
Here's the good news! You can get your report to lay out like you want once you get your data correct. In your report right-click on the Details section and choose the Format Section... option. (It's Section Expert in XI.) Down at the bottom, you'll see "Format with Multiple Columns". When you check that, you'll see another tab appear labelled "Layout". Use that to set the properties for the column. Unfortunately, I haven't had much like with the option "Across the Down", which is probably what you want, but try it and see if you can get it to work.
Drew