It does not.
Certain kinds of cards (such as flip cards, adventurer cards, and double-, triple-, and four-faced cards) define alternative characteristics for those objects under certain circumstances. Using these alternative characteristics doesn’t count as being modified.
Of course the card was never officially released and modified never officially defined so my answer is just best conjecture.
Louvaqs gatherer page rulings give us a definition of what it means to be "modified":
11/12/2019 A creature is modified if its text has been changed to modify its abilities, if it has gained or lost any abilities, or if a counter or an effect has set or changed its power or toughness.
Since leveler abilities are static abilities (710.2) that can change power/toughness and/or grant abilities, if they do either, then yes, leveling up a creature "modifies" it.
edit:
710.2 A level symbol is a keyword ability that represents a static ability. The level symbol includes either a range of numbers, indicated here as “N1-N2,” or a single number followed by a plus sign, indicated here as “N3+.” Any abilities printed within the same text box striation as a level symbol are part of its static ability. The same is true of the power/toughness box printed within that striation, indicated here as “[P/T].”
710.2a “{LEVEL N1-N2} [Abilities] [P/T]” means “As long as this creature has at least N1 level counters on it, but no more than N2 level counters on it, it has base power and toughness [P/T] and has [abilities].”
710.2b “{LEVEL N3+} [Abilities] [P/T]” means “As long as this creature has N3 or more level counters on it, it has base power and toughness [P/T] and has [abilities].”
edit2:
@genini2:
The level effects of leveler cards are not alternative characteristics, but static abilities changing power/toughness and abilities (see rule 710.2 above).
Notice Hexdrinker only counts as "modified" starting at Level 3. A level 1 or 2 Hexdrinker didn't gain any abilities or modified its P/T, just having a couple level counters ins't enough.
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Certain kinds of cards (such as flip cards, adventurer cards, and double-, triple-, and four-faced cards) define alternative characteristics for those objects under certain circumstances. Using these alternative characteristics doesn’t count as being modified.
Of course the card was never officially released and modified never officially defined so my answer is just best conjecture.
Since leveler abilities are static abilities (710.2) that can change power/toughness and/or grant abilities, if they do either, then yes, leveling up a creature "modifies" it.
edit:
edit2:
@genini2:
The level effects of leveler cards are not alternative characteristics, but static abilities changing power/toughness and abilities (see rule 710.2 above).
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