(I work on this for a living...)
Yes, it includes things like sea level rise. Having said that, the giant knob hiding in the math is the discount rate. If you have $1 of damage in 2121, how much are you willing to pay today to avoid it? $1? $0.01?
Discount rates are usually in the 4.5-6% range. On the lower end, that means damage 100 years out is discounted 80x+. Most of the hefty damage from climate change happens from 2060 onward in most models, so the NPV to society not actually that high (yet). You also have to decide if society will allow geoengineering (e.g. stratospheric calcite, or something that fairly harmless by contrast but politically charged today) when things get really bad.
(Realistically, that will likely happen because the alternative is much worse, so do you price that in? Something like stratospheric aerosols can turn back the clock for a significant fraction of damage (minus OA and some other nastiness))
Anyway, the $50/ton number is intentionally framed as a purely economic one, and it's acknowledged that not all externalities are captured, so you may want to pick a different number.
Also, as an aside, $600/ton isn't where the market is going, and not something to anchor on. I hope pyrolysis+sequestration, which has a lot of benefits, will get to a low cost point. They'll be competing with things in the $50-150/ton range, with various levels of scalability.