Actually, I can reproduce your demo t-SNE plots in JMP Pro ver. 14 with R 3.3.3 on Mac OS 10.13. The only error I get has to do with fonts, but otherwise it works.
More importantly, I actually wonder if it's suitable for my needs. I only have a few dozen samples at most and a few hundred features (i.e., proteins) at most. I'm thinking, then, that the t-SNE won't really give me a very different solution to PCA or MDS. In fact, it looks like it won't run at all: when I tried 12 samples x 94,000 genes with a perplexity of 5, it said the perplexity was still too high:
Error in Rtsne.default(inDataTsne, dims = 2, perplexity = 5, verbose = TRUE, :
Perplexity is too large.
Error in eval(expr, envir, enclos) : object 'outputY' not found
Unexpected errors occurred while attempting to transfer the data.
Issues found in R, could be caused by unsuccessful installation of Rtsne/umap packages or limited memory.
However, it also mentioned some R error, so I can't tell if it's my data's fault or R's fault!
Anderson B. Mayfield