How to differentiate a 100 & 200 tempo song?

Use a corresponding tempo text?

If I can give you an example : The french national Hymne "La Marseillaise" is a "MARCH" imagine a group walking with a "good" speed in playing music . It's in 2/4 or in 4/4, the tempo is 120 quater note by minute. Not 60 not 240. 120 is for a march, so if you have a slow music you choose rather 60, and a speed music rather 120, and for a very quick song, you choose about 200. It is not fine to draw the rythm of a slow song , with your hand at 120, and the rythm of a speed one at 60

Short answer: Be familiar with the rhythms of the genre, and tap your toes to it. If possible, read some scores from that genre. Your Nico puri example is ~200bpm in 4/4.

Way too long answer (terrible for a forum conversation, I know... sorry!):
You're completely right in noticing that you can write down the same music in different ways. You can e.g. double the tempo & halve all the note values, and if you hit play in Mscore the sound coming out of your computer will be exactly the same (at least if the metronome is turned off).
Your choice only becomes relevant when you want human performers to read & play it. Rhythms are generally interpreted, felt, and therefore played differently, depending on which count of the meter they fall on.
Also, often one choice of tempo & time signature is also by far the easiest to read & count, and most common/idiomatic for the style. This means the players can quickly notice patterns they are familiar with, and mentally compress all this information about the pitch & value of dozens of notes - sometimes even into "play the obvious thing for next 2 measures".
So the right answer is generally "whatever is more common in this sheet music of this genre". However, in some cases, there are legitimate disagreements and it comes down to opinion. This is more likely the further a style of music is from European classical, as it might not have a long tradition of being written down in our Western common practice notation system - or it isn't/wasn't commonly written down at all.

All that being said, your Nico puri example is definitely 200bpm. You can tell from the drums: The drummer plays variations of the standard rock beat, where the snare backbeat belongs on beats 2 and 4. Those are emphasized in basically all of Black music (blues, jazz, soul...), but due to its massive influence, also most of pop, rock, anglophone folk...
If it was 100bpm, most snare hits would land off-beat, on the ands between - those are not emphasized, at least in this genre (~pop-rock). (Might be different in e.g. reggae or latin? Far from being an expert there.)
(Side note 1: There is the skank beat in "rawer" punk/hardcore, which is mostly the same as the aforementioned basic rock beat, but played at double speed, so the snare lands on the off-beats, and you'd instinctively tap your toes along to the kick on 1,2,3,4. But you don't find them at 100 bpm.)
(Side note 2: Don't be surprised if you find stylistic elements in fairly mainstream Japanese music that would be considered rather "extreme" or unusual in Western common practice ("classical") & pop, as they seem to be very open to borrowing from "niche" genres: fast tempos from punk rock, virtuoso guitars & drumming from metal, complex extended chords from jazz, weird noisy synthesizers from EDM...)