Wow. He legit sounds like Sylvester here. To make those sounds, put your tongue to the roof of your mouth and don't allow air to come out of the front part of your mouth. All the air should be pushed between your molars and escape around your mouth, slightly vibrating your cheeks.
He sounds like that for the whole twitter interview that he just did. When his campaign was asked about it a bit ago, I think they made the one of the worst responses possible:
In an emailed response to an inquiry about the lisp from a Huffington Post reporter, the Trump campaign said, “Must be your s****y hearing. Get your ears checked.”
That's crazy! My most generous interpretation was that there was some sort of audio compession that was cutting off the S's. But to blame the listener is a classic move that shouldn't surprise me.
I reckon you're right, unless there was some additional audio equipement or network processing on Trump's side. But I think you're right that, at the very least, it wasn't something being done by the Twitter back-end.