Your 2nd solution is better structured than your working solution.

Code:

awk 'BEGIN { FS=OFS="\t" } { for (i=1; i<=NF; i++) if ($i~/^ *$/) $i="." } 1' input

It treats space characters as being empty, unlike your last solution that checks for being empty

Code:

awk 'BEGIN { FS=OFS="\t" } { for (i=1; i<=NF; i++) if ($i=="") $i="." } 1' input

---------- Post updated at 15:45 ---------- Previous update was at 15:12 ----------

Don's sed solution, after replacing \t with ${T} and putting the code in double-quotes, so the shell can substitute each ${T}.
For general safety I put the braces and escaped the $ (both not really required here).

Code:

T=$'\t'; sed "
s/^ *${T}/.${T}/
s/${T} *${T}/${T}.${T}/g
s/${T} *${T}/${T}.${T}/g
s/${T} *\$/${T}./
" input