If it is "on the" why is it not "sul computer"?

"We draw on computer" isn't strictly improper English. It takes the same form as: "We go by foot", "We are high on fame", "We were raised by hand". The omission of the definite article is sometimes done in English.

Although "we draw on computer" is slightly semantically different to "we draw on the computer". We draw on computer suggests we are digital artists; we draw on the computer could either generally mean we are digital artists OR that we draw on some specific computer.

"on a computer" is also good idiomatic English.