I am searching for a single word which represents "written from left to right" or "written from right to left". Please make sure that the word should be meaning not only the direction but also meaning direction in case of writing. I want to use it like "This language is X", where "X" is the asked for word.
In technical contexts (the study of scripts, Unicode's various rules for communicating them with computers, graphic use of textual elements) the abbreviations LTR and RTL are very often used.
There are boustrophedonic for scripts which change direction on each line, and words in Asian languages to distinguish vertical from horizontal (e.g. tategaki and yokogaki), but no single word I'm aware of for left-to-right or right-to-left though my reading would be such to make me well-placed to come across them if they existed.
Note also, that languages are not left-to-right or right-to-left, but rather scripts are: Malkuth and מלכות are the same word, and so in each case the language is Hebrew, but in the first case it is Hebrew in Latin script, while in the second it is Hebrew in Hebrew script. Likewise hedgehog and הדגהוג are both the same word, in English in Latin script and English in Hebrew script respectively. There are languages which are commonly found in more than one script.
Per Wikipedia, the standard terms for these directionalities are the quite obvious right-to-left and left-to-right, plus of course the ever-popular boustrophedonic. There are also top-to-bottom and bottom-to-top.
Unicode uses those terms for embedding control characters to change the direction of writing as follows:
U+200E LEFT-TO-RIGHT MARK * commonly abbreviated LRM U+200F RIGHT-TO-LEFT MARK * commonly abbreviated RLM U+202A LEFT-TO-RIGHT EMBEDDING * commonly abbreviated LRE U+202B RIGHT-TO-LEFT EMBEDDING * commonly abbreviated RLE U+202D LEFT-TO-RIGHT OVERRIDE * commonly abbreviated LRO U+202E RIGHT-TO-LEFT OVERRIDE * commonly abbreviated RLO