This isn't the reply you were hoping for but I tried my hand at seeing if it was a common format and sadly it isn't, it does look like a separate, new archive from the VPK.
Titanfall 1 used multilayered waves compressed within the VPK so I tried wav scanner to see if it was perhaps an uncompressed wave archive, no good. I then tried Ravioli game explorer and upon searching the contents it located 7 .swf but I don't think ravioli is accurate. I did a search on the .mstr format and discovered only one other game has used it which was the 2007 ps3 game lair? couldn't find anything else on it if anyone was able to extract it.
Looking inside HxD the offset of the .mstr file begins with
52 54 53 43 02 00 FF FF F0 FF 02 05 00 00 00 00
I'm not familiar with anything that begins with that.
I know you posted the whole file but I've included a small sample for others to analyze. Hopefully someone will be able to figure this out I really love the sounds in TF2 i'd love to add that to my collection!