And of course, the issue is that magic would be superior to guns for a very long time, while fulfilling the same purpose.
And gunpowder (or an equivalent) exists already, as there are references to cannons used on ships.
I picture more kinds of spells in Tamriel's future, like you said, magic would be superior to it. In real-life during the early years, you could have a bow, or a sword. In Tamriel they've already got magic, bows, crossbows, darts, swords, maces, axes, daggers, staffs, throwing stars, and a whole bunch of other things, I don't see why they'd say "We need more projectile weapons!"
I think if Earth had begun with magic that:
1. Technology would have advanced much more differently
2. Technology might not advance as much because we can already use telekinesis, levitation, water breathing, "unlock" spells, fire spells, healing spells, w/e.
The main thing is, when you have magic, it nullifies the need for there to be technological advancement in almost all areas. People on Earth technologically advanced because they had to, they needed the things. The Infant Mortality rate was huge, and people would die of diseases more often than wounds during wars. Thus, medicine was further developed (Alchemy and Restoration Spells). There have been technological wars between many countries, if you had the best weapons, you'd win. (Destruction Spells, Weapons that are already in Nirn). People needed to complete specific tasks like diving to the bottom of a lake. (Alteration Magic). People needed to get food, so they invented more technology for that too.
The last one, is where I think the most advancement would be. They still haven't perfected the art of harvesting, gathering, and cooking. In reality, if you had a "TES" world, the most development would be for leisure and food. You've already got all you need with magic, besides food, water, and companionship. So, people would build things to entertain themselves. They'd be more developed in exploration technology, more developed in recreational technology (although they could use magic for that too). The Dwemer were basically a lesson that technological advancement in a magical world leads to everybody blowing up into ashes. (Magic Nuke)
They don't need more protection, more offense, or more survival technological advancements, because they have magic.