If it's possible, I'd prefer to do it as a last-minute thing, rather than booking in advance. If it matters I do speak Russian, so it's okay if the tour is not English speaking.
The tour you've linked made by LDPR politic party and this is only for a Russian citizens.
However, here you can find a tour description which is done for foreigners too, and, maybe, you can also select a language (description said that you can pickup any language, but I don't think that it's really "any" :)). You probably should try to cantact the agency by email, contact information can be found here.
Address: Moscow, Nikolskaya st., 4/5, office 389. Phones: +7 499 39 810 29 +7 926 02 11 481 E-mail: firstname.lastname@example.org, email@example.com SKYPE tourincity
Update: it appears as none of travel agencies can actually do this tour for now. Can't say why is that, but right now I can't find any way to get into that building with excursion.