There are various nuances to take into account, depending essentially on what's in the mind of Mr. Senior. But a general answer would be :

You can't do anything, and you have no reason whatsoever to do anything about it.

There are two possibilities : either Mr. Senior is indeed too busy and is prioritizing some other work (going against Mr. Manager's request) because he knows it's the best course of action for him, or he just wants to slack off for a bit. In any case, you can't complain to Mr. Manager since he's away, and you obviously can't force Mr. Senior to do anything. You could complain afterwards, if Mr. Manager happens to come back from vacation before you leave, but that wouldn't make Mr. Senior work during his absence, and might burn bridges.

The thing is, I don't understand why you should bother with Mr. Senior when you can give your best with your fellow intern ? You're not going to be responsible for the future of the project. If Mr. Senior doesn't feel like getting up to speed and the project later suffers from it, it's not your problem, as long as you keep doing your job till the end of your internship.

Now, on to the "workplace politics" : if Mr. Manager ask questions regarding the lack of progress, you can simply tell him that Mr. Senior has been busy and couldn't allocate time to you, so you just did your best. It doesn't matter if it's true or not, you are just telling Mr. Manager what Mr. Senior said to you, without adding or insinuating anything else. You are not complaining about it, which makes you look professionnal, and doesn't officially put you in a bad spot with Mr. Senior. Of course, Mr. Manager will understand that Mr. Senior didn't do his part, and might take action, but it's either that or taking the responsibility for the lack of advancement on the project, which could be detrimental to the result of your internship (or not, but depending on your situation, it could be).

At this point, if Mr. Senior wants to resent you, there's not much you can do about it, and you probably shouldn't care because the person who might give a reference on your internship will probably be Mr. Manager, and not Mr. Senior.

Also, remember you are just interns : according to your formulation, you didn't know Mr. Senior before, and he didn't know you. He probably won't give a damn about you and will probably forget about you soon after you leave. You shouldn't think too much : if he doesn't want to help, so be it, it'll be more experience for yourself.