What factors, other than its homochirality, make our "brand" of biology unique?
I think the opposite list---what features of life might be reasonably expected to be the same elsewhere---would be much shorter. Nearly every feature of life on earth as I can think of it is arbitrary in the particular molecules.

DNA. Why only 4 bases? Why the bases that we have (ACTG)? Researchers are able to create organisms with expanded DNA alphabets even here on earth (1). Even if you believe that some form of molecular mechanism of heredity is a requirement for life, there is no reason it need be DNA. And while there has been plenty of controversy about arsenic-based life here on Earth, I don't see why there couldn't be arsenic-based life elsewhere.
Ribosomes. Why a combination of RNA and protein? There is a lot in the overall architecture of ribosomes that is locked in due to historical/evolutionary contingency, not any necessary feature of life.
The Central Dogma. Biology as we know it has certainly made great use of the ability to make temporary copies of messages, but I don't see why life orbiting Alpha Centauri would have to have arrived at a similar solution.
Phospholipid membranes. You could make the argument that some degree of compartmentalization is necessary for life to occur (to reduce complexity and allow evolution via drift and small-number effects to generate change), but I don't think they need to be phospholipids. I can also imagine all life on another planet contained within viral-like particles with purely protein (or some other alien polymer) coats.
Genes. Depending on the level one is arguing I can see this going either way. If a gene is just a modular set of instructions for a limited number of components, then perhaps this will show up everywhere---life on our planet is surprisingly modular, and it is hard to imagine life on another planet being able to get by without some modularity (though of course it is possible in principle). But certainly nothing is inevitable about the details of gene organization into promoters, coding regions (why a 3-base code?), introns and exons (I'm still surprised these exist on our own planet), operons, etc.

I think you get the idea. In fact, it's really hard to envision any feature of life on earth that doesn't smack of contingency in some way or other. Astrobiologists have held on to water as an essential ingredient for life as we know it, but still, that's &quot;as we know it.&quot;
I am really tempted to make some sweeping speculative statement about what features I might expect to be &quot;inherent in all possible biologies&quot; (a fascinating idea to think about), but that is way out of my depth. Right now I find it hard to come up with good candidates.
(1): Malyshev D et al. (2014). A semi-synthetic organism with an expanded genetic alphabet. Nature 509: 385-8.