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"OK, so I know that you two are always arguing about what type of crosswords to do-
'Normal crosswords are too boring!' 'Cryptics are too esoteric!!'
Trivia vs wordplay, yeah, I've heard both sides. But, I've also heard that you BOTH love video games, so here's what I've done:

Here are twenty crossword clues that describe twenty video games. Solve them if you'd like!
OR, if you treat each clue as cryptic wordplay (without a def) instead, you'll find a different video game as the answer for each clue!

Why don't you two work together for once, and when you get all forty written down, you can put the highlighted letters together to get one last clue. Which type of clue is that one? You'll see!"

 CLUE CRYPTIC ENUM / CROSSWORD ENUM

 1. Rogue tries to follow templar leader (6)/(14) 
 2. Law breaking, tasteless, sandbox entry (11)/(14)
 3. Scientific premise around martian origin? (6)/(10) 
 4. Not quite a rapper, weird kid (8)/(16)
 5. Man tossing bound article? (6)/(8) 
 6. Beginner to Hero: The planet rocks (11)/(10)
 7. Fantasy's heart found in Disney characters (7)/(13) 
 8. Try to escape from messed up monkey port? (7)/(11) 
 9. Soft and rosy, floating around; knotted thread nearly gone (14)/(14)
 10. On-rails shooting, space head destroyed (6)/(7)
 11. Determination, maybe innate, is lost (7)/(9) 
 12. Below the surface, with a late twist? (9)/(8) 
 13. Football with no sides, flipping the flipper? (14)/(12)
 14. Coins gathered, the hoarder follows a kind of maze? (16)/(10)
 15. Grim dead man losing afterlife, at first (6)/(12) 
 16. A jumping game with meat, odd no? (7)/(12) 
 17. The arrows nailed... there's non-existent dancing (9)/(20) 
 18. Divine butcher, roam around one greek fantasy (17)/(8) 
 19. Vehicle destruction with a ring: It has some co-op (14)/(4) 
 20. Crazy AI starts flinging female, trapped in lie (8)/(6)

Notes:

<sub>- Names of games and game-series are used. All are well known.

- Numerals at the end of game names have been culled (ie for a sequel
or if it was on N64)

- Enumerations are given, but do not separate out words. Will add if people are struggling.</sub>

Partial

Rogue tries to follow templar leader

Cryptic: TETRIS (T[emplar] + [TRIES]*)

Cross: ASSASSIN’S CREED

Law breaking, tasteless, sandbox entry

Cross: GRAND THEFT AUTO

Not quite a rapper, weird kid

Cryptic: PAPERBOY(?) ([APPER]* + BOY)

Cross: PARAPPA THE RAPPER

Beginner to Hero: The planet rocks

Cross: GUITAR HERO

Fantasy's heart found in Disney characters

Cryptic: DESTINY ([fan]T[asy] in [DISNEY]*)

Cross: KINGDOM HEARTS

Try to escape from messed up monkey port?

Cryptic: POKEMON ([MONKEY PORT]* - TRY)

Soft and rosy, floating around; knotted thread nearly gone

Cryptic: SPYRO THE DRAGON ([P + ROSY]* + [THREAD]* + GON[e])

On-rails shooting, space head destroyed

Cryptic: LA NOIR(?) ([ONRAILS]* - S[pace], missing an E though)

Cross: STAR FOX

Determination, maybe innate, is lost

Cryptic: METROID ([DETERMINATION - INNATE]*)

Cross: UNDERTALE(?)

Below the surface, with a late twist?

Cryptic: UNDERTALE (UNDER + [LATE]*)

Coins gathered, the hoarder follows a kind of maze?

Cross: SUPER MARIO

Grim dead man losing afterlife, at first

Cryptic: MADDEN ([DEAD MAN]* - A[fterlife])

A jumping game with meat, odd no?

Cryptic: MEGAMAN ([GAME]* + M[e]A[t] + N[o])

Cross: SUPER MEAT BOY

Vehicle destruction with a ring: It has some co-op

Cross: HALO

Crazy AI starts flinging female, trapped in lie

Cryptic: HALF LIFE (HAL + FL[inging] + LI[F]E)

Cross: PORTAL