Pretty much. Regular order sentence would be „Die Zeit läuft mir davon“, so I suppose this order, using the pronoun first, is to emphasise that it's an opinion.
It's one of the reasons I like German, you can have emphasis in written language as well as spoken language, simply by changing the order of things, whereas English is limited in that it requires intonation in speech and can't really be done in writing.
"for me, time is running out" moves the words and changes the emphasis (although not as much as putting it in italics). If you think about it, surround 'for me' with commas and you can put it anywhere in the sentence. To me English is more flexible as you can change the word order entirely and it is still understandable (even if it sounds weird). My (poor) understanding of German is that the word order is much more critical.
Isn't there a sort of antiquated English expression "time runs away with me" that means one has gotten distracted by something and has lost track of time? So might one say "Mir läuft die Zeit davon!" as an explanation for not getting around to doing something, or perhaps if one realizes one has stayed in a conversation too long and is now late for an appointment, etc.?
I am at the end of my wits with these "da words". I read the comments about the most correct translation would be "time is running away from me", which i could easily write "die Zeit läuf von mir", right? So why is the "da" element even there? What purpose does it serve? Other than impair intelligence recollection from the allies during WWII