It is kind of a strange sentence as far as figuring out where it would be used, but "Péter sees dinner" is perfectly fine English and sounds more natural than "Péter sees the dinner" to me unless there is something specific you want to say about the dinner. There are many exceptions, but articles are often dropped in English for meals, and this is often non-optional (especially if there is no additional emphasis or modifier (such as an adjective).)
"Names of meals normally do not take an article:
Did you have breakfast this morning? I'll have fruit for lunch. Let's go out for dinner tonight.
But if there is an adjective before the name of the meal or a phrase or clause after it, an article is used:
The breakfast that they served was fabulous. I had a quick lunch at Wendy's. That was the most delicious dinner I've had in a while."