It is unclear what plants are, but it does not matter here
The spellcasting rules let you only target an object, creature, or a point of origin for an area of effect.
Non-magical, ordinary flora plants by the game's rules are neither objects nor creatures (see below). Blight does not have an area of effect, so that leaves no way to target ordinary flora, but Blight says it can. This is a contradiction. Thankfully, there is a rule to address such contradictions:
Specific Beats General (page 7, PHB)
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 abili ties, 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 contra dicts a general rule, the specific rule wins.
In this case, the specific spell Blight tells you it can target normal plants, and therefore it beats the general object, creature, or spellcasting rules. It does not really matter what you consider them as, the spell tells you it works.
The definition of object that the game uses explicitly it limited to inanimate matter:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
Living plants according to this defintion cannot be objects, because animate is defined as "alive, possessing life", and living plants are alive.
What exactly counts as a creature is not sharply defined. There are bona fide plant creatures in the game, but they come with a creature stat block. They are defined as creatures with the plant [creature type][3 (Monster Manual, p. 7), which states:
Plants in this context are vegetable creatures, not ordinary flora. Most of them are ambulatory, and some are carnivorous.
Ordinary flora thus does not count as a creature with the plant subtpye.
In addition, there is the evidence from Fabricate, which says:
you can fabricate a wooden bridge from a clump of trees (...).
Creatures or magic items can't be (...) transmuted by this spell.
If trees were creatures, you could not use them for fabricate, but you can, so they cannot be creatures. Trees are a kind of non-magical plants, so non-magical plants in general cannot not count as creatures, if we believe Fabricate.
Points of origin
The spellcasting rules say (PHB, p.204):
A spell's description tells you whether the spell targets creatures, objects, or a point of origin for an area of effect (described below).
The areas of effect "described below" are cone, cube, cylinder, line and sphere. While you can target a point, you can only do so for spells that create one of these areas of effect.