...And investigate why it doesn't work.

Each StorageTimestampTest starts with a block that excludes non-WT storage engines.

I believe the code can refer to supporting snapshot reads instead, e.g:

        // Only run on storage engine's that support snapshot reads.
        if (!_opCtx->getServiceContext()->getStorageEngine()->supportsReadConcernSnapshot()) {
            return;
        }

However, a quick check showed Enterprise's inMemory failed the SecondaryInsertTimes test. I didn't try running the others.