Oh my, that is dismal.

Personally, I'd be inclined to ignore most of the machines, except the pull-down bar: lat pull-downs can be handy if you fancy working towards a pull-up.

And the levers for pushing and pulling forwards could be useful substitutes for chest presses and rows, if that's something you want to work.

in front of a mirror, but with no room to swing them or a bench to sit or lie on

Is there a free corner of space elsewhere in the gym? Nothing to say you can't move the weights around the gym, as long as you return them at the end of your session.

Is there enough space to lie down anywhere? (I'm thinking about Turkish get-ups, which are wonderful for almost everything. You may want to start these with your home weights or none at all, though; they make a light weight feel much heavier.)

If you've got standing room in front of the mirror, you can at least do squats, which should be excellent for hiking strength.

Also possible and fun, good for back and legs: windmills and one-legged deadlifts.

Btw, here's the Free, gratis and for nothing resource post.