As a single-classed Warlock, there are 2 main things that make the above build infeasible. The first is that it will take you 2 feats to be able to use Heavy Armour, and the second is that you can never obtain a Fighting Style. The good news is that you can still do as well for AC and almost as well for reliable damage. (The linked build gains very large damage increases on a crit, but outside of that the average damage from this build is only 3.67 lower.)
It's worth noting that you have the option of investing the feats to get heavy armour proficiency, since you are getting both a feat and an ability score increase. However, the better solution here is to use a Dex build instead.
With your point-buy rules, you can spend 12 points to get Dex 16, then 9 points to get Cha 15, then 5 to get Con to 13. The remaining point can go to any of your last 3 scores, it doesn't really matter which one. You then pick Drow for your race, which brings your Dex to 18 and your Cha to 16.
Starting ability scores: 8/18/13/9/8/16 (Any of the 8s can be the 9.)
At your first level, you take Warlock with Fiend Patron as planned. As with the linked build, you'll want the Eldritch Blast cantrip and the Hex and Hellish Rebuke spells. (Note that you don't actually need Eldritch Blast, it's just the backup option if you can't get into melee for some reason.) Use your starting gold to buy a rapier and a hand crossbow.
At second level, pick Armour of Shadows to bring your AC up, and either Agonizing Blast or Devil's Sight (depending on whether you want to improve your Eldritch Blast or get ready to use Darkness.) You'll also probably want to pick up Armor of Agathys, since it scales excellently as you level. (From 9th level onwards, it gives 25 temp HP, and more importantly, while it lasts creatures who hit you take 25 damage automatically.)
At 3rd level, take the Pact of the Blade and pick up Darkness.
At level 4, you can boost your Dex to 20 and take the Crossbow Expert feat. This allows you to attack with the rapier, then use your bonus action to attack with the hand crossbow. It's actually better than normal dual-wielding, because this way you can add your Dex bonus to the bonus attack. (Normally the Fighting Style is required for this, and you can't get it.)
At level 5, take the Thirsting Blade invocation.
At level 7, take Fire Shield and whichever of Devil's Sight or Agonizing Blast you didn't take at level 2.
At level 8, bring your Cha up to 18 and take the Sharpshooter feat.
At level 12, you want to bring your Cha up to 20, get the Lifedrinker invocation, and then take War Caster (so you don't have to worry about drawing and stowing weapons in order to cast spells. It also helps you maintain concentration.)
At level 16, you might as well boost your Con to 15, and I'd recommend taking the Elemental Adept(Fire) feat. (You lay down a fair amount of fire damage with Hellish Rebuke and Fire Shield, and you have access to some very powerful fire spells from your Fiend Patron.)
At level 17, take Foresight as your 9th-level Mystic Arcanum.
At level 19, bring your Con to 17, then take the Resilient feat, bringing it to 18. Resilient also gives you proficiency with Con saving throws, which will help you maintain concentration. (And they're one of the most common saving throws to have to make in the game anyway.)
Your attacks rolls with this build progress exactly the same way as with the linked build, except that you gain your stat bonuses much earlier, and if you delay taking Devil's Sight, you have to wait a while to get advantage.
Average Weapon Damage Rolls By Level (using Hex)
- Level 1: 1d8 + 1d6 + 4 [average 13]
- Level 4: [1d8 + 1d6 + 5] + [1d6 + 1d6 + 5] [average 26]
- Level 5: ([1d8 + 1d6 + 5])*2 + [1d6 + 1d6 + 5] [average 40]
- Level 8: ([1d8 + 1d6 + 5])*2 + [1d6 + 1d6 + 5 + 10] [average 50]
- Level 12+: ([1d8 + 1d6 + 5 + 5])*2 + [1d6 + 1d6 + 5 + 10] [average 60]
Average Eldritch Blast Damage Rolls By Level
(Assuming you took Agonizing Blast before Devil's Sight.)
- Level 1: (1d10+1d6) [average 9]
- Level 2: (1d10+1d6+3) [average 12]
- Level 5: (1d10+1d6+3)*2 [average 24]
- Level 8: (1d10+1d6+4)*2 [average 26]
- Level 11: (1d10+1d6+4)*3 [average 39]
- Level 12: (1d10+1d6+5)*3 [average 42]
- Level 17+: (1d10+1d6+5)*4 [average 56]
Average Hellish Rebuke Damage Rolls By Level
- Level 1: 2d10 [average 11]
- Level 3: 3d10 [average 16.5]
- Level 5: 4d10 [average 22]
- Level 7: 5d10 [average 27.5]
- Level 9: 6d10 [average 33]
- Level 16+: 6d10 [average 33.6]