Do baptists believe baptism did not pre-date Jesus Christ?

The short answer is, "they know that baptism pre-dates Christ."

Baptists are aware of the fact that baptism was practiced before Christ's incarnation, ministry, death, and resurrection. Baptists tend to a very literal interpretation of Scripture, and are well aware of the history behind baptism, and the fact that it's been practiced since well before Christ.

The difference, to Baptists is not "Baptism", it's "The Believer's Baptism". The Baptist doctrine of a Believer's Baptism doesn't teach that there is no other teaching on Baptism, it holds that the Believer's Baptism is the Baptism taught specifically in the New Testament for Christians.

From Baptist Disctintives

Baptists: Believer’s Baptism

“Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.” Romans 6:4

Ask most non-Baptists (and even some Baptists!) what is the Baptist distinctive and they likely will say, “Baptism of adults by immersion.” Of course, there is no one Baptist distinctive. Why then do many people regard baptism as practiced by Baptists to be our distinctive? A possible reason is that Baptists are one of the very few denominations which practice believer’s baptism by immersion and do so as a symbol of having been saved, not as a requirement for salvation.

In previous centuries, rulers of both state and church launched persecutions against Baptists for this practice. In the face of such harsh resistance, as well as the inconvenience of immersion, why have Baptists stubbornly held to the belief in and practice of believer’s immersion? The answer is found in basic Baptist convictions.

The Baptist belief is that pre-Christ, Baptism had different meanings. In some cases, it was a ritual purification, in others, a cleansing to prevent the spread of disease, etc.

From another source: Bible Believer's Baptist Church:

In Eph 4:5, the “one baptism” is the baptism by the Holy Spirit into the body of Christ.

In the Bible there are actually seven (7) different baptisms. And the only one that can save you is the spiritual baptism that you undergo when you receive the Lord Jesus Christ as your Savior. Not surprisingly, most religions teach some form of water baptism for salvation, thinking that all references to baptism have something to do with water and salvation.

Probably a better, more succinct version from Olivet Baptist Church:

The purpose of baptism has always been for identification. Long before John the Baptist, religious sects and secret societies required baptism as an official part of initiation or acceptance thus proclaiming ones identification as part of that group or sect. So long before Christian baptism, Satan had a counterfit baptism as explained so well by Rev. Hislop in his work called Two Babylons. Because the method was by immersion, and the purpose was for identification, this prevented what is currently practiced around the globe regarding infant baptism which is by sprinkling or pouring. This is why it is called, believers Baptism.

When you think about it, it's not that odd. Baptism has a different meaning to modern day Catholic teaching, vs. the LDS teaching vs. the Baptist teaching.

The article you're referencing is specifically speaking about the Baptist view on Baptism. (A Baptist will tell you it's the "Biblical" or "Christian" view on Baptism).

Thus is would be wrong to say that "Baptists don't believe Baptism existed before Christ", it would be accurate to say that "Baptists believe hat there are all sorts of teachings and beliefs around Baptism, and there were before Christ, but the Believer's baptism is the one described in Scripture".