I think it should be typing on computer

Actually there are two stances here. I understand your dilemma. The official website of XAT states that exam is to be conducted online, however upon calling the official XAT conducting authority, their response is that essay writing will still be offline. So the point is whether to go by the verbal terms as stated over telephone or the online mentioned terms.

I believe admit card will be issued tomorrow, so the admit card must clearly state how it is to be conducted exactly.

Hi Rahul! XAT would be a computer based exam from this year. While questions for all other questions have to be answered on computer with the help of mouse, essay writing question is the only exception. For this question, you will get answer sheets and you have to write the essay on the paper. For details, read the news below:https://bschool.careers360.com/articles/xat-2018-paper-based-essay-writing-despite-computer-based-test