I think part of it is the gamble that Suteguma's number could in fact be 8, but also that Baku could be wrong about everything and Suteguma's real number was below 8 all along. Going back to the old tables, if Suteguma had 5 or 6, Baku would have completely lost, and even died in the case of Suteguma's 5. If Suteguma had 7, this gamble could basically play out the same way, but Baku can't guarantee Suteguma had 7. That'd be why this was a massive risk, in my opnion.

Suteguma might just take the 50/50 chance and gamble, and Baku still has Marco and possibly Ranko on his side. It doesn't seem that risky for Baku to me. Since Suteguma wasn't sure of the password being 16 then that probably means that his number is 8, and so Baku would be able to win. But I suppose it's possible.

I guess it would end up with a lose-lose situation.
Suteguma can't find out Baku's number, and Baku doesn't have the strength to dominate the top of the tower and enter the password.

Yeah, I suppose that's true. But that would only tell Suteguma that he was lying, not exactly what his number was, since it could still be 8 or 9, and with Suteguma having only one chance it's not guaranteed that he'd just gamble on it. Sure, it's risky, but the worst case scenario is that Suteguma finds out Baku was making him think he had 6 or 7, but not Baku's exact number.

It's a risky move because if Suteguma was holding 8 beads
(Once Baku knew that 8 input was fake, Suteguma's number could only be 8 or 9, or else 8 can't be called a fake number),
then on his point of view, 7 would be the only number left in the 3rd round.
(He thought Baku's number was 6 or 7 after Baku entered 13, if Suteguma was holding 8, then the remaining number would be 8+6=14 and 8+7=15, but 14 had already been pressed by Suteguma in the second round.)

Then after Suteguma pressed 15 in the 2nd round, he would find out that Baku was lying.

When you put it like that it makes me think that Baku's number is 10 after all. There's still one thing that bothers me and still hasn't been directly addressed (AFAIK), and that is whether or not the Dotty considers numbers chosen with one of the two numbers being an excluded number due to a previous input as valid. In other words, is Baku's 13 input a valid input (with Baku's bead number being 10) considering that Suteguma chose 14 previously, thus eliminating 3 as one of his possible bead numbers (Eliminating 10+3 as a possible combination)? Or does the Dotty automatically take the eliminated possible numbers into account and expect the enemy to keep that in mind when entering their choice, making it an invalid input? I'd say that most likely the Dotty doesn't go that far, and only considers whether your input is valid in consideration of YOUR number only, which would make Baku's input of 13 valid even with 10 beads. This plays into what @Veshv mentioned about Suteguma's 14 input also "locking away" 13 as a possible choice for Usogui if he has 10 beads. Since although it was not explicitly stated that this sort of "impossible" input is valid in the Dotty, the price you pay for being wrong and gambling on it would be too great to attempt. Which would make perfect sense for Baku to gamble on just that! So yeah, if Baku's number is 10 then his 13 pick was an insane double layered gamble. If it turns out to be 8 or 9 then I don't really see why it would be a risky move, except for the part where he's trying to let Suteguma believe his number is 6 or 7, which would happen anyway.

I would say yes. The fact that Usogui chose 13 as the bluff is a clue as to what Baku's number is. Coincidentally, this was the biggest gamble for Baku as well, and I think you can understand why after deducing Baku's number.