Overrun adds a totally new way to move through an enemy space.
Overrun is listed in the "Action Options" section of the DMG (p. 271-272). It doesn't replace or (partially or fully) "override" any existing rules; rather, it supplements them by adding an additional way to move through an enemy space.
The general rule
The rule on moving around other creatures says, in part (emphasis mine):
You can move through a nonhostile creature's space. In contrast, you can move through a hostile creature's space only if the creature is at least two sizes larger or smaller than you. Remember that another creature's space is difficult terrain for you.
This is the general rule - normally, assuming that there is no more specific rule or game feature that contradicts it, most creatures can only move through a hostile creature's space if it's 2 sizes larger or smaller than that creature.
An existing exception
However, even without considering Overrun, there's already a specific race that overrides the size requirement of this general rule: halflings. The Halfling Nimbleness trait says:
You can move through the space of any creature that is of a size larger than yours.
This specific trait clearly overrides the general rule on moving through other creatures' spaces where the two rules conflict. Any creature could already move through the space of a hostile creature that is two sizes larger than it, so this trait makes it so halflings can additionally move through the space of a hostile creature only one size larger than it. It's not presented as an additional action option, just a specific benefit that overrides part of the general rule
Overrun is an additional action option with its own limitations
Likewise, the description of the "Overrun" action option says (emphasis mine):
When a creature tries to move through a hostile creature’s space, the mover can try to force its way through by overrunning the hostile creature. As an action or a bonus action, the mover makes a Strength (Athletics) check contested by the hostile creature’s Strength (Athletics) check. The creature attempting the overrun has advantage on this check if it is larger than the hostile creature, or disadvantage if it is smaller. If the mover wins the contest, it can move through the hostile creature’s space once this turn.
Consider that the rule on moving around other creatures already lets any creature move through a hostile creature's space an unlimited number of times, with the sole condition that the creature moving is at least 2 sizes larger or smaller than the enemy.
In contrast, Overrun expends an action or bonus action, requires a successful Strength (Athletics) check (on which you have disadvantage if you're even 1 size smaller than the enemy), and lets you move through the enemy's space only once on that turn even if you win the contest.
If Overrun was still forced to abide by the size restriction of the regular rule on moving around other creatures, then it would just be flatly worse than the regular rule. If that were the case, then it wouldn't be an additional action option - no creature would ever use Overrun, since they'd just be risking failure and wasting an action/bonus action for no benefit. (And if the idea is to replace the regular rule entirely, such that creatures can't move through a hostile creature's space at all without using the rule, then the description of Overrun would need to explicitly say so.)
Rather, the point of Overrun is to add an additional option to the game. Without it, if a player asks whether their Medium-size character can move through the space of the Medium orc or the Large troll in front of them, the base rule just says the answer is no. With the Overrun action option, however, the DM can say, "You can, but you'd have to pass an Athletics check and spend your action or bonus action to do it."
Overrun effectively has no meaningful impact if the hostile creature is already 2 sizes larger or smaller than you; as mentioned above, you can already move through such a creature's space without expending anything.
(And regardless of size, another creature's space (whether friendly or hostile) is still difficult terrain for you, as stated in the rules on difficult terrain.)
Tumble doesn't care about size either
The same logic applies to the "Tumble" action option (DMG, p. 272) as well. Tumble uses nearly identical phrasing to Overrun; it requires spending your action or bonus action, and involves contested Dexterity (Acrobatics) checks by you and the hostile creature, but there is no automatic advantage/disadvantage on the check based on size. Thus, as an additional action option, Tumble also does not have any size-based restrictions on who can attempt to do it.