Yoshi pointed out the correct problem, ToT uses the sprites by default.
There are two types of units sprites, though:
1) animated unit sprites (unitXX.spr). These can simply be turned off by disabling unit animation in the ToT game menu (graphics options).
2) static unit sprites (static.spr). These are pretty much always used, even when unit animation is turned off. This'll be what's causing the problem. There are several ways to solve this problem:
Edit the rules.txt, specifically the @UNITS_ADVANCED section. With one of the flags there you can override the .spr files for each unit individually.
If you're making a scenario, and you want to turn off all sprites anyway, there's a better way. Instead of editing the rules.txt, use the Cheat menu. Go to Cheat > Scenario Parameters > Edit Special Rules and set the .SPR file override to 1.
If you also want to disable unit/resource animations, first
disable those options in the game menu, then set the lockout values in the special rules to 1. This is because lockout does NOT disable the animation per se, it simply locks whichever option you set in the game menu.
Finally, you can create your own static.spr
using a utility I made called SpriteGen
(also see my homepage/signature). That way you don't have to override the .SPR files, you only have to turn off unit animation.
More importantly, SpriteGen allows you to hide the unit shield (for say impassable terrain or fixed objective units in a scenario), something that isn't possible otherwise.