Depends which kind of content you are going for. This guide seems to be aimed at trials (or the target dummy), so it's missing a lot of important stats for overworld (questing, delves, public dungeons, world bosses etc.) which are usually provided by supports in your group.

The Bow/Bow build that @BasP linked is by far the best one for purely single target organized trial groups, but I would recommend first getting something more universal.

Right now Velothi Ur-Mage's Amulet is by far the best mythic for templars (and for almost every other class), and it's better than any monster set out there. So drop the Zaan and use 1pc Slimecraw instead.

Set wise, for solo content and dungeons you want to be on light armor for the extra penetration it provides (Whorl of Depths, Mora's Scribe, Order's Wrath (crafted)) and then on a second set which can be many things like Deadly Strikes, Aegis Caller, Pillar of Nirn, Sul-Xan just to name a few.
A good 'slot and forget' set up is Deadly Strikes paired with Whorl of the Depths. Note that the Minor Slayer from Depths or any other trial set does nothing in overland content, so if that's what you are mainly doing, Order's Wrath would probably do better. For a beginner trial setup I would recommend the same sets, but with Deadly Strikes on the body and Whorl of the Depths front barred with either Maelstrom Greatsword or Inferno staff, or Master's Bow on the back bar.

As for the skills, for most content I would replace the trap with Camouflaged Hunter (provides the same 3% weapon damage buff from Fighter's Guild plus Minor Berserk and Major Savagery/Prophecy). Do this only if you are using Velothi, since it provides you the Minor Force buff with 100% uptime.
On the backbar I would go with an Inferno Staff, since you will be needing all the barspace you can get. Skills: Wall of Elements, Solar Barrage (5% damage to class abilities), Elemental Susceptibility (Major Breach + Status effects), Ritual of Retribution, and the last one is a flex slot which depends on the type of content you are doing. Options and example situations for the flex slot: Degeneration (use this if you are on Tri-Stat potions and doing content where killing the bosses takes longer, but you don't have a Dragonknight with Igneous weapons in the group), either morph of Rune Focus (depending on which resource you have harder time sustaining. Use this when you are taking more damage and want to be tankier (world bosses etc.), Caltrops (simply more AoE damage, slot when you have nothing better to put here).

Using weapon or spell power potions will be easier for your barspace and offer more freedom to slot different skills. Major Brutality from jabs is enough if the execute phase lasts less than 10 seconds. So delves, public dungeons, normal dungeons etc.



I feel like I missed something really important, but I can't think of what it is...

Never heard about plitzzy.com, will not open link.

Well, the goal with a Stamplar build is to stack Spell Damage as high as possible. Any Fighters Guild skill on your frontbar will raise it by 3%. You probably know this, but its significance can not be overstated.

You'll probably do not want to use Vampires Bane. The damage output is low and scaled with the Buff in mind and not only the DoT. It'll turn out to be something on the 1k to 2k DPS range, depending on your crits. So, not very good.

In my experience the key to Stamplar DPS is sustain of the Magicka side of things. It will need to be high enough to cast at least three, possibly four, Magicka DoTs until execute begins. And of course it'll also allow you to start beaming earlier, and so get higher DPS earlier.
In that context it is possible to run Channelled Focus instead of Rune Focus, for that extra Magicka sustain. Alternatively, using Candied Jester Coins can provide a bigger boost, but you need to run Rune Focus in that case, to keep the balance.