Any like that?

Crusader: No Remorse ;-)

But seriously, wouldn't most D&D games in which you can roll your character qualify since you should be able to play a Paladin in most of them?

The First Templar
Knights of the Temple I and II
Ember (you are a "Lightbringer", close enough...)
Diablo 2 and 3 (you can pick Paladin and Crusader respectively)

If Inquisitor also qualifies, then:
Inquisitor
Heretic Kingdoms: The Inquisition
Dragon Age: Inquisition

I assume you are mostly after games where you are simply given these characters to play as, and not games where you create a character from scratch. Otherwise, all games that include any of those classes in any way, shape or form could be mentioned here.

Wars and Warriors: Joan of Arc

Vampire the Maquerade, Redemption

Paladin's Quest

Baldur's Gate you can be a paladin

Dante's Inferno

Actually, no; you play as a mage in that game (who just happens to be able to use a sword because main character).

Final Fantasy 4, on the other hand, might qualify, at least after a certain point in the game.

In Pathfinder: Wrath of the Righteous, it can be argued that your main character is a crusader of some sort, regardless of your path, mainly because the game is so focused on fighting a war against demons. Then again, some of the mythic paths might cast doubt on that issue (if you want to retain the crusader theme, I would go with Angel or Aeon). Worth noting that Pool of Radiance would be an exception, as there's no paladin class in that game (though cleric is an option).

The Dark Sun games wouldn't work either, as there's no paladin (IIRC), and templar exists only as an NPC class.

I believe you can't currently play as a paladin in Baldur's Gate 3. (You can in Solasta, if you want to play something like the 5e paladin right now; no DLC required for this class.)

The Quest For Glory series has paths that your main character can take to become a Paladin. From QFG2 and onward there are opportunities to advance to the Paladin class.

If I might ask what the quantifications for these nebulous titles are?

Because in Avernum, you can make a custom character class, and these four seem to suggest there's something specific about them.

King's Bounty: The Legend (you can choose paladin)
Aion (you can pick the templar class)
In Black Desert Online the valkyrie is more or less a paladin (with awakening you get a big lance)

I would believe that you can create a full party of Paladins in the D&D (Forgotten Realms/Krynn) games available here, if you wish so, no?
At the very least, you can create one Paladin (and deem that to be your main character).

Lost Eidolons is one. And maybe Symphony of War. I am stretching the definition here but, in the end, you could say the heroine is a holy warrior