There are so many replies focused on what time you 'should have' turned up, etc. I think the root cause is that you are not as close to your sisters as they are to each other, so I suggest this is something you consider working on (unless you don't want it). Perhaps it is worth talking to your sisters and calmly mentioning it, and how it made you feel.
Are your sisters closer to each other because of their age, or are they at a different stage of life than you, i.e. they have older children? Or are they both united by not having children, so see you as being different? It could simply be family dynamics in that they see you as the little sister and, in some unkind way, less important and so deserve less respect. Only you would know the truth.
I think it was wrong of them to start without you, especially if it was for a formal get together such as a birthday dinner. Although some posters have pointed out that you were rude for not having arrived sooner to join in with the drinks, I disagree. You did not even know about them and you did not receive a message from either sister about meeting up earlier. Other posters have also mentioned that it's normal to meet up for the pre-dinner drink. What if you did turn up for the 'standard' pre-dinner drinks at 6:15pm, and there wasn't one and no-one else had turned up? That would be a bit of a waste of time.
I think your sisters were inconsiderate and, if you care enough, perhaps it's worth getting to the root of why they see and treat you in this way and take action to improve your relationship with them. It is possible it's nothing in their eyes and they think you are happy with the status quo which is why they continue to treat you in like this.