All roads lead to S4N4
Yes, you are indeed right in the comment section that the reaction between thionyl chloride and ammonia will give trace amount of tetrasulfur tetranitride(1) and the intended product is thionyl imide ($\ce{HNSO}$)(2).


From the 'thionyl chloride' entry from the same site you used
in the question:


  Thionyl chloride reacts with ammonia giving rise to various complex
  products, the nature of which varies with the conditions.

As said, the main product from the reaction in gas phase is thionyl imide and trace amount of thiazyl chloride($\ce{NSCl}$) and sulfur dioxide. The reaction are as follows:


$$\ce{SOCl2(g) + 3NH3(g) -&gt; HNSO(g) + 2NH4Cl(s)}$$
$$\ce{HNSO + H2O -&gt; SO2 + NH3}$$

Ref. : Inorg. Chem., 1977, 16 (1), pp 216–217
DOI: 10.1021/ic50167a050