You like me, don't you with 〜のこと好き

Grammar Explanation: Referring to a person with 〜のこと

Ran is walking through town. A smug young man in a sharp suit has fallen into step beside her.

男(おとこ):: 「オレのこと好(す)きなんだろ？」; “You like me, don't you?”
蘭(らん):: 「てめーマツキヨＣＭのチンピラかよ？」; “What are you, some punk out of a Matsukiyo commercial?”

Key Points

1オレのこと好(す)き

のこと after オレ makes him the person the liking is aimed at. オレのこと好(す)き means “you like me”.
The full form is オレのことが好(す)き. In casual speech, the が often drops.
With 好(す)き, のこと is optional. オレが好(す)き means the same thing, but the のこと version is common in conversation.

2なんだろ presses for agreement

なんだろ is a casual なのだろう. な links the na-adjective 好(す)き to んだ, and だろ with a rising tone asks the listener to confirm: “You like me, don’t you?”
The question assumes the answer, which is what makes it so presumptuous.

3Ran’s rough reply

てめー is a hostile “you”. かよ at the end of a question adds scorn: “What are you, some…?”
マツキヨ is short for Matsumoto Kiyoshi, a drugstore chain, and ＣＭ is a TV commercial. チンピラ is a small-time punk.

てめえ (You (rough)): てめえ is a rough, hostile word for “you”, used in anger or to pick a fight. It is often written てめー.
オレ (I): オレ is a katakana spelling of おれ, a casual, masculine word for “I”. It is also written 俺(おれ).
こと (Thing): こと is an abstract thing, matter, or fact, as opposed to a physical object. It also turns a verb phrase into a noun, as in 見たことがある. It is also written 事(こと).
好き (Liked): 好(す)き describes something you like or someone you love.
チンピラ (Punk): チンピラ is a small-time thug or a young hoodlum who acts tough.