If there is a verb "laufen", then the negative is "nicht laufen". In German sentences, the verb usually goes in the second position. In that case, "nicht" follows the verb (after time indicators, perhaps). If the verb is moved to the end of the sentence because it's in a subordinate clause, then move "nicht" to the end of the sentence, right before the verb again.
Ich laufe nicht ins Park. (I am not running in the park.) Am montags will ich nicht laufen. (I do not want to run on Mondays.)
spazieren means to walk lauf means to run. I guess the Germans use them as a kind of synonym. Like in English if you say "I gotta Dash" does not mean you have to run away, but that you have to leave. some walk away, some run. Like saying "I gotta bail" some might mistake bail for bailing water, or needing bail to get out of the slammer, whereas others mean they have to leave.
The usual placement of "nicht" in German sentences is at the end, only followed by infinitives or participles, if there are any.
A possible exception is, when it is not the whole sentence that is negated, but only a particular phrase. In this case the "nicht" immediately precedes this phrase.
There are several ways to negate a sentence in English. This one puts the negative in the verb phrase. When negating a verb phrase you need to use a helper verb, such as "do". The negative goes after the helper verb and before the main verb. I do not run.
If you put the negative at the end an American English speaker will feel misled because first you said you run and then you changed your mind by the end of the sentence.
Simply put, because that's how it is. Languages develop and then form standards. In German many verbs change their inner vowel in 2nd and 3rd person singular. E.g.
ich laufe, du läufst, er/sie/es läuft, wir laufen ihr lauft, sie laufen
ich spreche, du sprichst, er/sie/es spricht, wir sprechen, ihr sprecht, sie sprechen