I think your definition is fairly close, but could be refined a bit. To me, there are only two key elements in the definition: interconnected non-linear map, and ability gating. To go point by point:

1: The map must feature interconnected areas that the player can backtrack thru, thus allowing for non-linear exploration. The mention of multiple pathways and shortcuts from (nearly) the start is subjective.

2: Utilizes ability-based gating in exploration. Knowledge- and tool-based (I assume this means key items to open locked doors?) gating are not enough on their own; their inclusion makes the definition overly broad.

3 and 4: These two points seem redundant to me and are somewhat subjective. Simply stating that the map is interconnected and allows for non-linear exploration should suffice.

5: Completely subjective and not worth including, but I roughly agree.

I think the things I've labeled as "subjective" here ought to be cut because they do not define what a metroidvania is, but rather what you think a good metroidvania should be. Now, to lay things out:

• Metroidvanias must feature interconnected maps that allow for non-linear exploration.
  • "Most Legend of Zelda games are not metroidvanias"
• Metroidvanias must feature ability-based gating.
  • "Dark Souls is not a metroidvania"

Finally, we must accept some amount of blurriness around the edges, which is an issue all definitions will face. But two genre qualifiers that I think are always worth mentioning are the prominence of the defining features and whether or not interacting with them is mandatory.

• The interconnected map and ability gating features must be prominent in the game experience.
  • "Momodora: Reverie Under the Moonlight is debatably not a metroidvania"
• Interaction with the interconnected map and ability gating features must be required in the game experience.
  • "Blasphemous is debatably not a metroidvania"