Regarding the speed of this film, my understanding is as follows...
The ISO of a film is not purely a characteristic of the film itself. It depends on the film, the developer, and the specific development process used. The speed for that combination of factors is determined by measuring the difference in negative density for a given difference in exposure. This is then rounded to the nearest standard speed found in a table in the ISO spec.
So-called box speed is the maker's recommended exposure index for a given film, developer and process. Since changing developer and/or process can change ISO, it's up to the maker to set their criteria for how the film is rated, such as the most linear response to a given brightness range in the subject, ability to retain shadow detail when under-exposed, and so on. In other words, box speed tends to be the maker's recommendation that will best lead to whatever quality of the film they want to emphasise.
In the Kodak datasheet for TMax films, P3200 is rated at 1000 with certain developer and process combinations, and 800 with other combinations. The combinations that yield the slightly higher rating have then been adjusted to a nominal 800 when rounded to the nearest standard speed in the ISO table. It would appear that Kodak chose this speed for reasons other than supporting the high speed aspect. They don't give the reason(s), but the datasheet says that when rated at 3200 (ie, exposed and developed differently), there will be some loss of shadow detail, and a slight increase in contrast and graininess.
To me, this suggests that the 1000 or 800 'true' speed was established as a result of characterising and adjusting the exposure/developer/process combination until certain criteria were met (such as image quality, shadow detail, linear response, etc). However, this stuff is not considered in the ISO rating - that is concerned with difference in negative density for a given difference in exposure. Consequently, if a maker wants to promote a film as a high speed one, they are at liberty to mess around with higher EI settings and different developer/process combinations as they see fit, and declare that the film is rated at whatever speed they feel satisfies whatever it is that they want to promote.
So, what is the box speed of P3200? A further look at the TMax datasheet reveals that the 100 and 400 films are rated at those speeds "in most developers", while P3200 is described as a multi-speed film. The non-committal wording notwithstanding, the nomenclature of the TMax films is perhaps telling. The 100 and 400 films are called 100TMax and 400TMax, while the '3200' is called P3200TMax. The 'P' prefix seems to me to be important - my guess is that it signifies that the film is suitable for pushing to 3200. Perhaps more importantly, if the number on the box - industry wide - usually indicates the nominal EI to be used in conjunction with a given developer and process, then 'P3200' isn't a number, it's a label or a name. Arguably a bit of marketing fluff, but only if you see 'box speed' as something that meets certain arbitrary criteria that aren't required by the ISO spec. Maybe P3200 doesn't have a box speed, or the box speed is the 1000 / 800 given in the datasheet for results that satisfy certain criteria, or, if we seek to use it in the manner promoted by the maker (ultra high speed), we could say that it's 3200 (other speeds are available, but that's what is implied by the nomenclature).
Ultimately, it's a moving target - all film speeds are, and more so with this because it seems to be very tolerant in terms of producing 'acceptable' images for a wide range of EI and developer/process combinations.
The usefulness of referring to a box speed for this film is perhaps down to what photographers agree it should be - but that will depend on what they use it for. It could be an 800 film with good image quality, or a 3200 with acceptable image quality. It is somewhat equivalent to say that it's an 800 that can be pushed, and that it's a 3200 that can yield 'even better' image quality when pulled.
Personally, I'd call it a 3200. If I bought it, it would be because I'd be interested in using it at that speed - 3 stops more than my normal fast film of 400 is a big change that would allow me to shoot in conditions where the 400 would struggle. Others may prefer to use it at 800 and get better image quality, but the extra stop over Tri-X doesn't tempt me.
Addendum
Looking at the datasheet some more, the packaging artwork for the then-current datasheet (2007) is given, and that's what I refer to above. However, the previous artwork is also given. In that, the films are explicitly rated thus...
100 - 100 ISO / 21 DIN
400 - 400 ISO / 27 DIN
3200 - 3200 ISO / 36 DIN
However, the 3200 also has three boxes...
[ 1600 P1 ]
[ 3200 P2 ]
[ 6400 P3 ]
The 'Pn' designations perhaps indicate the number of stops that it can be pushed, which again implies that the nominal speed is 800. For that older packaging, however, Kodak do clearly give the box speed as 3200 (the newer packaging doesn't have the explicit ISO / DIN - just the name or label).
What we'll see on the reissued film remains to be seen.