Minor Magic says:
A rogue with this talent gains the ability to cast a 0-level spell from the sorcerer/wizard spell list. This spell can be cast three times a day as a spell-like ability.
Spell-like abilities can only qualify for requirements that specifically call out the spell name, otherwise they are not considered being able to cast spells, as can be seen on this FAQ:
Does a creature with a spell-like ability count as being able to cast that spell for the purpose of prerequisites or requirements?
Only if the pre-requisite calls out the name of a spell explicitly. For instance, the Dimensional Agility feat (Ultimate Combat) has "ability to use the abundant step class feature or cast dimension door" as a prerequisite; a barghest has dimension door as a spell-like ability, so the barghest meets the "able to cast dimension door prerequisite for that feat. However, the barghest's dimension door would not meet requirements such as "Ability to cast 4th level spells" or "Ability to cast arcane spells".
The bolded part is exactly the requirement for Arcane Strike:
Prerequisite: Ability to cast arcane spells.