Well, I can run pdflatex manually without problems on a tex file with epsfig included. That's why I'm wondering, why TextMate cannot use pdflatex, even if I configured it to do so.
The engine that is used to compile you document is determined by the packages you use: "epsfig", which is an old package (and has been superseded by graphicx) usually indicates that the document is of 2.09 vintage, and will most likely require dvips to compile. At least I guess that's the logic behind the code in "TexMate.py" which decides which engine to use. I would imagine that trying to determine whether it's a modern document running a compatibility mode of an ancient package is going to get really old really quickly for the poor maintainer! I think it's time to convince your co-authors to shed their epsfig dependency and come into the 21st century! (Well, at least the 1990's...)
The example file you posted doesn't actually include an eps file, and if you try to compile it by simply substituting an eps file for the jpg you used it'll produce an error under pdflatex: "! LaTeX Error: Unknown graphics extension: .eps."
In short: using epsfig for inclusion of jpg's is, well, sufficiently funky/perverse that I wouldn't expect TextMate to bother trying to work out that it's *possible* to compile the thing under pdflatex.