In Dark Souls, Pyromancers are generally seen as one of the "DPS" classes.
In the original Dark Souls games, Pyromancy worked purely off the item called "Pyromancy Flame" which worked very similarly to many other weapons. The power of your Pyromancy depended purely on your Pyromancy Flame level.
In Dark Souls 3, however, they changed the Pyromancy Flame so that it worked more off your stats, like most other caster builds. However, because this works off both your Int and Faith, it does make reaching the full potential of your spell casting harder (soft levels of 40, to a maximum of 80 over two stats instead of one), but with the payoff of a higher overall potential.
Additionally, it is important to note that while most enemies don't sport resistance to fire, most of the more unique enemies do, and only a handful of them (like the Pus of Man enemy) have a weakness to fire. In these instances, it is important to have a backup option to be able to deal with these particular enemies.
In regards to damage dealing, while Intelligence and Faith contribute directly to your Pyromancy, Strength and Dexterity contribute to your ability to deal physical damage.
The starting equipment for the pyromancer includes the handaxe, which is a versatile tool, scaling off both Strength and Dexterity. It boasts a decent damage return, and can be two-handed, to increase the damage by 1.5 x your Strength modifier, and also has the "Warcry" ability, that can deal an additional 10% damage for 30 seconds. And an added bonus is that your Strength stat also adds to your fire resistance as well, which can come in handy.
Dexterity on the other hand is a more well-rounded stat, that contributes to all defenses and resistances (though at a much smaller return per level), but can also decrease your spell casting time (which stops at level 50). Unfortunately, however, this does interfere with the damage output of your handaxe (the 1.5x multiplier for two-handing and the Warcry ability work purely of your Strength stat), but if you use a Sharp Gem you can increase the bonus you get from Dex scaling, if you wish.
Ultimately, how you wish to play is completely up to you.
Dark Souls is a versatile game, and you can either play to your own strengths, or build a character that is specialised in a particular area. For a new player, Vigor and Endurance are important, as they contribute to your HP and Endurance bars respectively, but ultimately, with time and experience, they actually can become less important, as with timing and patience, players can often play the game effectively with minimal scaling in these stats.