It’s a euphemism. The rule for using “a” or “an” is based on pronunciation, not spelling. Since “euphemism” starts with a consonant sound ("you" sound), we say “a euphemism”.
We typically use the article “the” to introduce a range of leisure activities and forms of entertainment (e.g., “to the beach”, “to the mountains”, “to the movies”, “to the disco”, “to the opera”, etc.).
In normal conversations, we commonly use the expressions “do the dishes”, “do the laundry”, or “do the housework”. We can omit the article to put the emphasis on the activity rather than the items to be washed or cleaned.