Almond milk does not have the fat that cow’s milk has, so your pudding will not be set up properly. This will hold true for any milk alternative.
That said if you would like to take a longer route there is a simple workaround that could help you to create these using a dairy-free alternative milk. If you use boxed cook and serve style pudding, you can use a thickener (like cornstarch) to help make the mixture thicker.
Using cook and serve pudding will take longer to cook and cool so the prep time for these shots would be greatly increased.