Your second attack uses general two weapon fighting rules(Ch-9).
The Martial Arts feature is explicit about the special nature of the second attack in bullet 3.
When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action. For example, if you take the Attack action and attack with a quarterstaff, you can also make an unarmed strike as a bonus action, assuming you haven’t already taken a bonus action this turn.
It does not say "you can make one unarmed strike or a monk weapon attack" as a bonus action. Since you are not using that special Monk feature, in that your question says "instead of bullet three" you revert to the general case of two-weapon fighting. (For "specific beats general" see below)
Any PC can use generic Two Weapon Fighting from Chapter 9 which specifically removes the dexterity bonus from the second attack.
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
Naming convention: WoTC Arrgghhh! moment
This is a common point of confusion due to a name choice. The general two weapon fighting versus two weapon fighting style. Only the Ranger and the Fighter get the Two Weapon Fighting Style.
When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack (p. 27, Basic Rules)
It is unfortunate that they used the same term for two subtly different features. One is unique to two martial classes, the other is usable by any PC/NPC. If they could have called the fighting style "Two-Handed Fighting Style" to differentiate it from the general "two weapon fighting" this confusion might be alleviated.
Specific beats General: does something break if Monk gets this benefit?
Hard to say. We are talking one average damage difference for a pure Monk at low levels, and a hope to trigger a Sneak Attack (and keep bonus damage) for your multi-classed Monk/Rogue(Arcane Trickster). Since you did not clearly identify how many levels of Monk and how many levels of Rogue(AT) you are using, this assessment can't cover all cases.
This book contains rules, especially in parts 2 and 3, that govern how the game plays. That said, many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins (Basic Rules, p. 5)
Class features are in Part 1 of the rules, and those specific rules beat general rules.
When appealing to "specific over general" which rule is specific and which rule is general? (T.J.L has offered one analysis on this in his answer, in terms of the Monk rule not being specific enough as compared to the Ranger/Fighter fighting style). So too does guildsbounty, in greater detail
... many racial traits, class features, spells, magic items,
monster abilities, and other game elements break the general rules in
You can make an argument that the specific class feature of Monk breaks the general Two Weapon Fighting Rule that applies to all other classes, or, you can argue that the Monk rule is a variation on the finesse weapon rule that applies to weapons other than light / finesse, such as clubs, hand axes, quarterstaffs and maces. (T.J.L. seems to make the latter point). All simple weapons (that don’t have the two-handed or heavy property) are Monk weapons.
You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.
The argument is that what makes this Monk class specific rule overwrite a general rule is that all simple weapons are Monk weapons(that's not a short list) so now a Club, Handaxe, Javelin, Light hammer, Mace, Quarterstaff and Spear, all use the Dexterity bonus for attack and damage. This provides a Monk a flexibility not available to any other class in terms of applying Dex where Str is usually the case. (And if an improvised weapon is ruled as being a club, then at higher levels that club becomes a monk weapon and its weapon damage increases as monk damage increases ...)
Compare Finesse to the Monk class feature.
Finesse. When making an attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the attack and damage rolls. You must use the same modifier for both rolls.
The ruling needs to come from the DM since it is not clear which is the specific rule that supersedes the general rule. If you really want this, then I recommend that you make this appeal to your DM on the basis that the Monk class feature is more specific (as a class feature) than the general rule on two weapon fighting (Ch-9) since short sword is a Monk Weapon by that class feature. Be prepared for a ruling that looks at it the other way: that the Monk class feature isn't specific enough and is specific over general in a different sense: some bludgeoning/slashing weapons get Dexterity bonuses to hit and damage where normally Strength is the ability bonus for that.
At first level applying this ruling would put the monk in the same damage output range of a two weapon fighting style fighter. At second level, this matches the Ranger with that choice. By the time your Arcane Trickster arrives at level 4, (assuming 1/3) the other two have an ASI and you don't have one yet.
At level 5, you either get an ASI or a feat or another level of monk (ki) and the other two classes now have two attacks.
A note on the two other martial characters, Ranger and Fighter, who have to choose their two weapon fighting style at the expense of Archery, defense, Great Weapons Fighting, etc. A problem can be that, with this ruling, the Ranger or Fighter had to make a sacrifice (pick that fighting style over any other) while the Monk had to make no such choice. That may be perceived as a problem at your table by other players, and it may not. Discuss this at your table and with your DM.
By 5th level your Monk damage for the unarmed attack matches the short sword and renders it moot, and at 6th level all of your unarmed strikes are magical attacks. That may be more important, getting that hit against resistant and immune monsters. Discuss with your DM; I'd be inclined to rule in favor of it unless someone at the table perceived that your character was getting an advantage they did not.
Sneak Attack damage, as a Rogue, tends to overwrite the Dexterity bonus as you gain levels in Arcane Trickster. By the time you choose AT, sneak attack is 2d6. At level 5 it is 3d6 and so on. The higher the level the less important that dex bonus is to your damage bursts.
You only trigger Sneak Attack once on your turn, so you can't get that 2d6 twice if you hit twice; you can get it once if you hit once in two attacks. Even at low level, one trigger of sneak attack damage is typically more than the Dexterity bonus.
How long will this game last? As your Rogue levels go up, and sneak attack damage goes up, so the burst damage opportunities go up.