How to define (logically) the complement language?
You aren't exactly correct in your example because of the redundant negation of the $\leq$ sign. In the most general sense, we always have:

$$\neg (x_1 \land x_2\land ...\land x_n)=(\neg x_1) \lor...\lor (\neg x_n)$$

Meaning: NOT (A AND B AND C...) equals (NOT A) OR (NOT B) OR (NOT C)...

In your case, we have two conditions with an AND between them:


M is a Non-Deterministic TM
M has an accepting run on $w$ of length $\leq |w|$


Finding the complement of the language requires negating these conditions, and therefore getting the language where either:


M isn't an NDTM, OR
M is an NDTM , BUT, it doesn't have an accepting run on $w$ of length $\leq |w|$


Notice the difference in the negation of the second condition - we changed it from having a run satisfying a certain property to not having a run satisfying the same original property.

From my experience, usually in these kinds of questions you have a language composed of TMs/Automata/etc' fulfiling a certain condition, and in such cases the negation would be everything which isn't a TM/automaton/etc', PLUS everything which is of the correct "type" but doesn't fulfill the original given condition.