The thing is that what happens is both. When the area is moved onto the creature, the creature then has entered the area. That the area is the one doing the moving doesn't matter -- you can enter a thing while remaining sedentary if it comes to envelop you. A critter that swallows you whole as it moves into your space is certainly something you "entered." If a gelatinous cube falls on your head from orbit, you have definitely "entered" it, even though you're not moving.
I think justifying that interpretation is getting into the realm of semantic gymnastics when a simpler interpretation suggests itself.
It may be more productive to compare Moonbeam with the damage-on-move interpretation to similar 2nd-level spells and see how it would compare over the course of the duration. Flaming Sphere is a pretty obvious spell to compare it against, as some others have already done. I'll just highlight the differences between them.
Range: FS 60 feet; M 120 feet.
Components: FS V; M V, S, M (no cost)
Area: FS effectively 15-foot-diameter (5-foot-diameter but affects adjacent squares); M 10-foot-diameter
Damage: FS 2d6 fire at end of creature's turn if it remains adjacent (limited number of creatures could end their turn adjacent, 56 damage (2d6 * 8) if we say medium creatures pack in around it for some reason); M 2d10 radiant when a creature moves into (once per turn) or starts its turn in the area (44 damage (2d10 * 4) if we say its area is filled with medium creatures, possibly more if creatures choose to congo line through it on their turns for some reason)
Movement: FS 30 feet as a bonus action, can ram a creature to inflict 7 (2d6) damage; M 60 feet as an action, every creature it moves over takes damage (potential 264 (2d10 * 24) if it sweeps horizontally over an area jam packed with medium creatures, such as an army formation, even if it only sweeps over 2 creatures that is still 22 (2d10 * 2) damage, creatures aren't able to avoid this damage by moving away).
Other: FS has some limits to where it can move due to terrain, M is less restricted; M is a cylinder, doesn't seem to be ground based so potentially has greater utility against fliers; M has additional utility against shapeshifters.
Situational considerations aside, looking at this comparison I don't see many reasons to use Flaming Sphere instead of a damage-on-move Moonbeam - I don't see many reasons to use Flaming Sphere against Moonbeam as I interpret it, for that matter. The only drawback would be that you'd need to be careful about moving the Moonbeam over allies, but Flaming Sphere has limitations of its own in that regard. There is also the point raised above by Shadowdweller00, that the 3rd-level Call Lightning seems to be marginalised by Moonbeam, even without the move-on-damage interpretation.