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The damage listed in Flame Hammer's skill description is the "blast" damage. This is the crater that the skill leaves behind briefly when you use it. When you spend a charge on the skill, it creates 2 additional craters ahead of you with a bit of space between each.
The additional craters will only spawn 3 splinters and the splinters they create have fixed distance (no bonuses from the tiers).
Here's a video to demonstrate (lvl 15 flame hammer). Note that the initial impact spawns more projectiles that travel longer: https://files.catbox.moe/m54njv.webm
In any case, Flame Hammer should be significantly stronger against single target due to the projectiles turning around.
Third, Flame Hammer will always hit the initial target for the melee strike + all the splinters. The additional projectiles from spending a charge, seem to spawn further away and do not hurt the initial target. I am not sure about the charge behavior at higher levels.
(cont)
You can verify the following by enabling console and smacking a dummy or you can install the GUTS modding tool (that comes when you buy this game) and check the game data for this.
The description in the guide about Flame Hammer is mostly correct. The game's description is highly misleading.
The damage listed in the game is from the MELEE HIT. The splinters do half this damage and convert it to fire. By right, the game should show "Secondary Hit: 32% weapon damage as fire" at lvl 1 like in say Shadowshot's description, but the devs forgot.
(cont later)
Flame Hammer for example is much more powerful than Emberquake. What you computed is not correct because Flame Hammer's splinters do 124% of dps weapon each and not just the half. And Strength is much more efficient than Focus to improve both skills.
You also didn't mention that only Flame Hammer cast speed can be improve. Emberquake is a slow skill and will always be.
Also Heavy lifting is absolutely useless since dual wielding is always better for the engineer than using a 2H weapon. The benefit of getting 8 slots for gems using Netherrealm weapons and new enchants outshines easily the use of a 2H weapon.
There are other skills I didn't test yet.
Several of the Engineer's abilities also ARE worth putting one point in, depending on your build & how many buttons you are willing to push from time to time. Ember Hammer will 100% break shields on enemies, even with just one point, which can be very, very useful for any Engineer using melee attacks. You poo poo Charge Reconstitution, but Forcefield isn't realistically going to be up all the time on Elite difficulty and having this extra bit of healing happening every time you use a charge can be quite good for many builds. And Coup de Grace is just plain good synergy with a lot of the Engineer's active skills - I find it is worth getting 1 point to speed up leveling with Seismic Slam, or for the synergy with Heavy Lifting.
So, it could potentially deal 3 times the damage you calculated if you manage to hit everything on a single target.
In practice, you can usually hit 1~2 blasts and like 70% of the splinters, which still gives it far superior single target damage to emberquake when using charge.
However, emberquake is undeniably better for AoE, and it still has the advantage of not using charge, so both has their uses, and could be used in the same build if one has the points to spare.