Approach via organism characteristics:
The key constraint is obligate aerobe causing infection in a burn patient.
Among the options:
- $\text{Pseudomonas aeruginosa}$: obligate aerobe, gram-negative rod, motile -- classic burn wound pathogen
- $\text{Meningococcus}$: facultative anaerobe
- $\text{Streptococcus pyogenes}$: facultative anaerobe
- $\text{Pneumococcus}$: facultative anaerobe
$\text{Pseudomonas aeruginosa}$ produces pyocyanin (blue-green pigment), pyoverdin, and exotoxin A. It is gram-negative, motile with polar flagella, oxidase-positive, and the leading cause of burn wound sepsis. It is the only obligate aerobe among the choices.
\[\boxed{\text{Pseudomonas aeruginosa}}\]